This paper proposes a single-shot high robustness wavefront sensing method based on deep-learning for wavefront distortion measurement in high power lasers. This method could achieve fast and robust wavefront retrieval by using a single-shot near-field profile image and trained network. The deep-learning network uses fully-skip cross connections to extract and integrate multi-scale feature maps from various layers and stages, which improves the wavefront retrieval speed and enhances the robustness of the method. The numerical simulation proves that the method could directly predict the wavefront distortion of high power lasers with high accuracy. The experiment demonstrates the residual RMS between the method and a Shack-Hartmann wavefront sensor is less than 0.01 µm. The simulational and experimental results show that the method could accurately predict the incident wavefront distortion in high power lasers, exhibiting high speed and good robustness in wavefront retrieval.