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In the constant voltage driver for stepper motor control, the motor cannot rotate properly under the high-frequency environment, so current hysteresis control circuit is designed based on LMD18200. This paper describes the common forms of the stepper motor power amplifier circuit firstly, and analyzes the difference between constant voltage and constant current driver circuit, and deduces the characteristics of steady current and fluctuation frequency theoretically. Comparing the rising slope of phase current between constant current driver circuit and constant voltage driver circuit through Matlab simulation, the average output torque and operating frequency are explained. Two kinds of drive hardware circuit are achieved with motor driver integrated chip LMD18200, and tested separately under the condition of using the same motor type TS3641N1E2. At different operating frequency, according to the phase current and operating state of the two driving circuits, the design of constant current driver circuit is verified to meet the requirements for the control of space remote sensing mechanism.