In order to obtain a second-order mathematical model of the ball screw feed drive systems in the designing stage, this paper proposed a simulation modeling method based on model reference adaptive system. In this method, a parallel model reference adaptive system, which regarded the mechanical model as the reference model and regarded a second-order model as the adjustable model, was designed use only input and output measurements based on Popov’s hyperstability theory. And the second-order model’s parameters could be achieved by simulation. The proposed method was confirmed effective through case study. The results show that: the second-order system’s parameters can be identified correctly, and the output of the mathematical model can be followed preferably by the second-order system. The error is less than 0.02mm.