According to the preliminary requirements of hard X-ray free electron laser (HXFEL) for offset mirror group (the meridian shape error is less than 0.5 μrad before bending and after clamping), the traditional mechanical bending is difficult to meet and can be corrected in real time, so the structure of piezoelectric side-placed piezoelectric bimorph mirror (PBM) is adopted. The mirror is placed horizontally, and the voltage needed to correct the low frequency surface shape error caused by dead weight is calculated by singular value decomposition (SVD) method, and the feasibility of the scheme is verified by finite element analysis method. Different bending surface shapes are solved and analyzed, and then thermal analysis method is added to solve the surface shape mutation caused by local radiation. The simulation results show that in the case of dead weight, the initial slope error of the mirror is 242.43 nrad (root mean square, RMS), and the slope error can be greatly reduced to 7.743 nrad (RMS) after voltage bending correction. When adjusting the target shape, the slope error between the actual bending shape and the target shape is only 0.0024 nrad (RMS).