In order to improve the performance of unimorph deformable mirror for astronomical adaptive optics applications, an unimorph deformable mirror with edge-driven was proposed. The unimorph deformable mirror has a 75 mm diameter and 214 elements, which is supported by several piezoelectric stack actuators at the edge. First, the structural model was established using finite element method. The performances of unimorph deformable mirrors with three and six active supports were analyzed and compared. Then, a three points edge-driven unimorph deformable mirror and a six points edge-driven unimorph deformable mirror were fabricated. Finally, the correction performance of the supporting actuators for low aberrations was tested using a wavefront sensor. The experimental results show that, the unimorph deformable mirrors with three and six supporting actuators can reconstruct tip and tilt aberrations which are greater than 12 μm under 100 V operating voltage with normalized residual error less than 0.06. Six supporting actuators also have a good correction capability for astigmatism and trefoil aberrations. It is proved that the supporting actuators at the edge can be used to improve the correction capability of the unimorph deformable mirror.