Laser thermal stress forming, which is a contactless and highly flexible manufacturing technology, can minimize problems such as springback, cracking, and wrinkling caused by mold or tool manufacturing, thus providing a precision manufacturing solution for microcorrugated sheets. However, microcorrugated sheets are prone to edge effects due to the uneven distribution of energy input and constraint differences during the scanning process. Because of the multipass and multicycle scanning involved in the laser thermal stress forming process of microcorrugated sheets, the surface distortion and residual stress caused by the previous scanning affect the thermal deformation in the subsequent scanning. This effect is amplified by the superposition of edge effects during multiple scanning, which exacerbates the instability of microcorrugated sheet forming. Therefore, the suppression of edge effects in the laser thermal stress forming of microcorrugated sheets should be a major focus. In addition, the mechanism of the surface distortion caused by multipass coupling is complex. In this study, the effects of laser process parameters on the edge effect are analyzed by numerical simulations and experimental studies. A varying velocity round-trip coupling scanning strategy is proposed to suppress the edge effect and is also applied to microcorrugated sheet forming, as this provides a reference for the analysis and suppression of edge effects in multiple scanning. The heat accumulation and displacement distribution at the free end after scanning are analyzed through numerical simulations under various scanning strategies. An experimental platform of laser thermal stress forming is constructed. The specimen used in the experiments is 304 stainless steel sheets with dimensions of 30 x 30 x 0.4 mm. The study employs a 500-W oscillator continuous fiber laser with a laser power of 150-450 W, velocity range of 10-70 mm / s, and scanning number range of 5-20. Response surface analysis (RSA) is used to analyze the effects of different laser process parameters on the edge effect. Suppression of the edge effect using the varying velocity round-trip coupling scanning strategy is then conducted, and the displacement of the free end of the forming sheet is determined. To observe the local morphology of the formed end of the sheet, a local 3D solid contour is acquired using confocal microscopy. According to the RSA, laser process parameters are critical factors that affect the deformation of bending parts. The smallest change in relative angle with constant-velocity scanning are obtained when the scanning number and velocity are 15 and 50 mm / s, respectively. Furthermore, the results show that a varying velocity strategy (an early-stage scanning velocity of 30 mm / s combined with a later-stage scanning velocity with 50 mm / s) exhibits a smaller change in relative angle as compared with constant-velocity scanning (a scanning velocity of 30 mm / s), with a reduction of approximately 63.0%. Based on the suppression of the varying velocity strategy, a varying velocity round-trip coupling scanning strategy is proposed, and the mechanism of edge-effect suppression under different strategies is investigated by numerical simulations and experimental studies. The study finds that the varying velocity round-trip coupling scanning strategy effectively reduces terminal heat accumulation and improves the temperature field distribution in the scanning process. Both the round-trip and varying velocity scanning strategies can improve the edge effect within a certain range of processes. In addition, the coupling of these two strategies can achieve further optimization because the temperature fields at both ends of the sheets can be controlled. Furthermore, the relative angle change is reduced by 77.8% using the varying velocity round-trip coupling scanning strategy. Finally, laser thermal stress forming of trapezoidal corrugated sheets with depth-width ratios of greater than 0.75 is achieved. Under this strategy, a flat profile appears on one side of the trapezoidal corrugated sheet wall, and a smaller height difference can be observed in the flow channel forming. Both numerical and experimental results reveal that round-trip scanning restrains the edge effect in the forming by balancing the temperature field at the beginning of the scanning line, whereas the varying velocity suppresses the end displacement height by reducing the terminal heat accumulation at the scanning line. Laser process parameters are also significant factors that affect the deformation of sheets. In summary, the varying velocity round-trip coupling scanning strategy can effectively suppress the edge effect of forming parts and realize the precision forming of microcorrugated sheets with large depth-width ratios, thus providing a reference for high-quality microcorrugated sheet forming.