Many existing parametric probabilistic wind power forecasting methods cannot achieve good performance due to adopting inaccurate forecasting models. Therefore, in this paper, the random-approximation technique and the ADMM algorithm were employed to develop a non-parametric probabilistic wind power forecasting method, namely, the random-approximation based probabilistic wind power forecasting (RA-PWPF) method, which is able to approximate any non-linear forecasting model without specifying the form of the true forecasting model in advance. The proposed method and the parametric method were compared in terms of the forecasting performance through simulations conducted on a real wind power data set. The simulation results showed that the average forecasting errors of the proposed method and the parametric method are 0.02423 and 0.03097, respectively, and thus the former outperformed the latter. Then, the effectiveness and the superiority of the proposed method were verified.