The tensegrity structure is prestressed spatial structure composed of rods and cables. Its multistable phenomenon brings great research potential in energy storage and robotic. In order to completely analyze the changes of configurations and mechanical property in stable state transformation (SST) processes of multistable tensegrity structures, a whole-process tracking (WPT) method based on Levenberg-Marquardt method is proposed. Three numerical examples are calculated, and the WPT is successfully realized, which proves the feasibility and universality of proposed WPT method. According to the calculation results, the variation of the driving force and elastic strain energy during SST are further summarized. Alternatively, different types of driving-paths are investigated, the results show that mechanical property during SST could be adjusted effectively by modifying the driving-path. The proposed WPT method and analysis results provides insights for designing and implementing multistable tensegrity structures.