Wavefront reconstruction is of great importance in adaptive optics. Accuracy of the reconstruction has a significant effect on performances of an adaptive optics system. An adaptive algorithm for wavefront reconstruction based on a reference-free Shack-Hartmann wavefront sensor is proposed. In this approach information needed for wavefront reconstruction, including the detection windows, the actual centroids, the reference centroids, and the reconstruction area, can be automatically determined according to characteristics of obtained spot field of Shack-Hartmann sensor. The effects of different reference centroids on the reconstruction result of the incident aberrations are discussed. The reconstruction algorithm is experimentally verified by compensating phase distortion produced by artificial atmospheric turbulence in laboratory through an adaptive optics system. The experimental results show that wavefront aberrations caused by the atmospheric turbulence can be reduced to below 0.1λ, which makes the quality of images close to the diffraction limit. The wavefront construction algorithm is an attractive and practical alternative to an adaptive optics system for telescopes.