This study proposes the design of a hybrid reluctance-actuated fast steering mirror (HRAFSM) using Maxwell's electromagnetic normal stress principle. Strain gauges were attached to the flexible supports as sensors for measuring the rotation angles. According to Maxwell's stress tensor theory and the theory of vibration mechanics, we obtained the dynamic equation of the HRAFSM in the uniaxial direction to investigate the relationship between the input current and the output angle of the entire system. Further, we propose a control algorithm combining proportional-integral-derivative (PID) and adaptive inverse control (AIC) to achieve high-precision control. We established an experimental system for testing and validation of the control method. The experimental results showed that the designed HRAFSM can achieve the expected rotation angle of ±1.5 mrad, and revealed a linear relationship between the rotation angle of the two axes and their corresponding strain voltages. The effectiveness of the designed controller was verified, and the amplitude tracking errors of the x- and y-axes were 0.1% and 0.14%, respectively.