To improve the starting quality of automated mechanical transmission (AMT) as a soft starter for belt conveyors, a novel data-driven method is proposed. By analyzing the common soft-starting acceleration curves, a segmented acceleration curve is proposed as the soft-starting acceleration curve for AMT. A modified model free adaptive control (MFAC) method with jerk compensation is proposed as a data-driven method to control the AMT output shaft’s angular acceleration, which consists of a MFAC algorithm and a jerk compensation algorithm. Simulation comparisons are analyzed between the modified MFAC method with jerk compensation, the prototype MFAC method, and the proportion integration differentiation (PID) method. Results indicate better control of the modified MFAC method with jerk compensation on the AMT output shaft’s angular acceleration than the other two methods. It also has excellent properties of small tracking error and small shock, providing a novel approach for AMT as a soft starter.