Fast steering mirror platform which is composed of piezoelectric ceramic has hysteresis characteristic, it affects the control of the fast steering mirror. In order to control fast steering mirror effectively, open loop control method based on Prandtl-Ishlinskii(PI) inverse model was adopted. Firstly, the PI model was used to build the mathematic model of the hysteresis characteristic of the fast steering mirror and the parameters of PI model were identified by least mean squares method; Secondly, the parameters of the inverse model of PI were solved based on the reversibility of the PI model; Lastly, the effectiveness of the open loop control method based on PI inverse model was verified. According to trajectory tracking experiment data, in the case of sine wave trajectory, root mean error is 1.23% and maximum error is 2.45%; in the case of triangle wave, root mean error is 1.3%, maximum error is 2.37%. It proves that open loop method based on PI inverse model is feasible and can effectively control fast steering mirror.