The Naiver-Stokes equations are utilized to investigate the bubble dynamics subjected to the flow speed in the vicinity of a rigid wall. The predictions are compared with the Gilmore method and available experimental results, and a reasonable agreement is obtained. The important flow properties, e.g., bubble morphology, collapse time, jet development, pressure wave propagation, and vorticity evolution are studied in detail. The results demonstrate that the combined effect of the flow speed and rigid wall results in the generation of oblique jet, which may contribute to the development of the fish-scale pits on the surface of the hydraulic machinery. Moreover, our results show that the impulse loads caused by the bubble collapse in moving water are lower than those in stationary water. Finally, it is indicated that the stretching term plays a major role in the vorticity both inside and outside the bubble, while the dilatation term mainly influences the vorticity inside the bubble.