We propose an analytical nonlinear hysteresis model of the bimorph beam bending piezoelectric actuator for a deformable mirror system. An explicit solution is derived from the analytic method based on the nonlinear elasticity. As an application example, the nonlinear hysteresis behaviors of a bimorph beam bending piezoelectric actuator, which is sandwich compounds consisting of a lower and an upper piezoelectric ceramic (PZT8-50) layer and a middle layer made of the aluminum alloy, are examined with the model. The numerical calculations based on the analytical solution are presented. The numerical simulations have shown that the nonlinear hysteresis behaviors of the bending actuator are depended on the start values of the exciting electric field and the geometric parameters of the metallic layer. In addition, the numerical results have also shown that the thickness of metallic layer has little influence on the relative hysteresis, and the relationships between relative hysteresis Δd  /  ΔD and the driving electric field   |  E_start  |   are linear.