Magnesium phosphate cement (MPC) has emerged as a rapid-setting repair material widely used in various emergency reinforcement projects. When MPC is applied in road repair, it's important to assess the quality of repaired pavements through the strength of the material, especially the compressive strength in our research. To ensure the structural functionality of rehabilitated pavements, Non-destructive testing (NDT) techniques are highly recommended, for the reason that the pavements could stay integrated and workable while being tested. In this study, we fabricated 206 sets of MPC specimens of different ages, and the ultrasonic-rebound combined method was raised to test the MPC material, from which we got the rebound hammer (RH) values, the ultrasonic pulse velocity (UPV) values and the values of the material's compressive strength. To predict the compressive strength of concrete (fc), a variety of machine-learning methods are used through making use of the input parameters (R and UPV in this study). Here, a model named LAC, which integrates Long Short-Term Memory, convolutional layers, and attention mechanism has been proposed for estimating the compressive strength of concrete. Compared with other state-of-the-art and classic machine-learning methods, the proposed model obtained the optimal statistical indexes on the test set, including R-2 value delivered 0.98. The study showed that the proposed model is efficient while predicting the compressive strength of concrete with the ultrasonic-rebound combined method.