Abstract: The conventional extreme learning machine (ELM) is sensitive to outliers. Aiming at the shortcoming, this paper proposes a robust extreme learning machine based on p-power Welsch loss. Firstly, the mean square error loss of the conventional ELM is replaced by the p-power Welsch loss to enhance the robustness of the proposed algorithm; Secondly, the l₁ norm regularization is introduced into the objective function to reduce the complexity and improve the stability of the ELM network model; Moreover, a fast iterative shrinkage-thresholding algorithm (FISTA) is adopted to minimize the objective function so that the computational efficiency can be increased; Finally, the performance of the proposed method is verified by means of synthetic data and UCI datasets, which shows that the proposed algorithm can attain stronger robustness, better stability and lower training time.