Based on the need of compensating middle and low order aberrations which lie in solid high power laser system in the future, optimal design and simulation analysis about edge-driven mirror are done. The design frame of four-arm edge-driven mirror is put forward, and the simulation model is built. Aimed at the residual error root mean square (RMS) and peak to valley (PV) value, the influence of structural parameters on the performance of correcting low order aberration is analyzed. According to the residual error RMS and PV value curve of correcting focus astigmatism, coma with structural parameters changing, the optimal parameters of the model are chosen and corresponding residual error RMS and PV values are shown. The simulation and calculation results show that for focus at 20 μm, astigmatism at 10 μm and coma at 10 μm of PV, the residual error correcting focus, astigmatism and coma are 0.2366 μm of RMS and 1.3762 μm of PV, 0.0112 μm of RMS and 0.1146 μm of PV and 0.1606 μm of RMS and 0.9773 μm of PV, respectively. These data prove that correction performance of four- arm edge- driven deformable mirror satisfies the demand of design.