The wavefront distortion occurs when vortex light transmits in atmospheric turbulence, so wavefront correction is required. Compared with the traditional adaptive optical system with wavefront sensor, the adaptive optical system of the wavefront sensorless using a stochastic-parallel-gradient-descent (SPGD) algorithm has the advantages of simple realization of hardware and good adaptability of complex environment such as light intensity scintillation. The simulation results show that the system can correct the wavefront distortion and improve the mode purity for single-mode and multimode multiplexed vortex beams. The experimental results show that the intensity correlation coefficient of single mode vortex beam can be increased to around 0.85, the intensity correlation coefficient of multimode multiplexed vortex beam can be increased to around 0.72, and the wavefront distortion correction effect of single mode vortex beam is better than that of multimode multiplexed vortex beam. Both the simulation and experimental results show that the adaptive correction technique using SPGD algorithm can effectively realize the wavefront distortion correction of vortex beam.