Abstract: In order to improve the control performance, a new prescribed performance function (PPF) was proposed for Hammerstein system where the hysteresis nonlinearity was described by Prandtl-Ishlinskii (PI) model. Based on the PPF, the tracking error can be transformed into transformed error to converge a prescribed neighborhood. Moreover, a prescribed performance adaptive controller was designed and the control law was derived. Next, an appropriate Lyapunov function candidate guarantees the stability of the Hammerstein system. Finally, theory analysis and simulation results demonstrate that the proposed PPF not only restrains the hysteresis effectively, but also achieves the high precision control.