This study presents a Fuzzy Integral Sliding-Mode Control (FISMC) approach for the high precision motion control of Fourier Transform Spectrometer (FTS) based on Michelson interferometer. In this motion system, the system parameters are nonlinear and time-varying because of the mechanical design. To deal with these problems, a new control strategy which implies a FISMC for the speed loop and a Proportional-Integral (PI) control for the current loop is used to track the desired Optical Path Difference Velocity (OPDV) accurately. A Sliding-Mode Control (SMC) is designed to enhance the robustness of the system and reduce the influences of the time-varying disturbances. The integral in the sliding-mode surface is utilized to reduce the steady-state tracking error. Moreover, a fuzzy logic controller is served as a gain factor to suppress the undesired chattering introduced by SMC for the steady tracking. Finally, simulation and experimental results demonstrate the effectiveness of the proposed FISMC for the precision control of FTS.