A feature-based phase retrieval wavefront sensing approach using machine learning is proposed in contrast to the conventional intensity-based approaches. Specifically, the Tchebichef moments which are orthogonal in the discrete domain of the image coordinate space are introduced to represent the features of the point spread functions (PSFs) at the in-focus and defocus image planes. The back-propagation artificial neural network, which is one of most wide applied machine learning tool, is utilized to establish the nonlinear mapping between the Tchebichef moment features and the corresponding aberration coefficients of the optical system. The Tchebichef moments can effectively characterize the intensity distribution of the PSFs. Once well trained, the neural network can directly output the aberration coefficients of the optical system to a good precision with these image features serving as the input. Adequate experiments are implemented to demonstrate the effectiveness and accuracy of proposed approach. This work presents a feasible and easy-implemented way to improve the efficiency and robustness of the phase retrieval wavefront sensing.