Model wavefront-sensorless adaptive optics(AO) system has a great application potential because of its fast convergence and good correction. It is important for correction effect and convergence of AO system that how to generate basis functions and determine its number of order. Eigenmodes of deformable mirror(DM) were used as basis functions in this paper. AO simulation platforms were set up with a 32-element DM, a 88-element DM and a 127-element DM respectively and the correction effect and the convergence rate were investigated. Results show that AO systems can obtain the correction capability close to the ideal correction of DM, which indicates the correction capability of DM are utilized fully. Additionally, because the number of DM eigenmodes is equal to the number of DM actuators, it is not necessary to determine the required number of modes no matter how the strength of the aberrations is. The convergence speed of AO system only depends on the number of actuators of DM.