Against the background of increasing installed capacity of wind power in the power generation system, high-precision ultra-short-term wind power prediction is significant for safe and reliable operation of the power generation system. We present a method for ultra-short-term wind power prediction based on a copula function, bivariate empirical mode decomposition (BEMD) algorithm and gated recurrent unit (GRU) neural network. First we use the copula function to analyze the nonlinear correlation between wind power and external factors to extract the key factors influencing wind power generation. Then the joint data composed of the key factors and wind power are decomposed into a series of stationary subsequence data by a BEMD algorithm which can decompose the bivariate data jointly. Finally, the prediction model based on a GRU network uses the decomposed data as the input to predict the power output in the next four hours. The experimental results show that the proposed method can effectively improve the accuracy of ultra-short-term wind power prediction.