To correct the phase aberrations in a wavefront, a wavefront sensorless adaptive optical (AO) system is set up. A real-number encoding Gaussian mutation genetic algorithm (GA) that is adopted to control a 61-element deformable mirror (DM) is presented. This GA uses the light intensity behind a pinhole on the focal plane as the objective function to optimize, and therefore to omit the procedure of measuring the phase aberrations in the laser wavefront by a wavefront sensor. Phase aberrations generated by the DM are brought to an ideal incident wavefront. Several correction simulations have been accomplished. The simulation results show that the genetic algorithm is capable of finding the optimum DM shape to correct the phase aberrations. After the phase aberrations of the wavefront have been corrected by GA, the peak light intensity on the focal plane can be improved at most by a factor of 30, and the encircled energy Strehl ratio can be increased ultimately to 0.96 from 0.032. It is also found that the convergence and stability of the 61 voltages on the DM is quite well. The simulation results prove that the genetic algorithm can be used in AO systems effectively.