Curve smoothing plays an important role in both Computer Aided Geometric Design and related manufacturing industries. In this paper, considering discrete digital curve is looked as non-stationary signal, a novel method of filtering discrete digital plane curves based on Bivariate Empirical Mode Decomposition (EMD) is presented. Firstly, separate the variables of the discrete plane curve, and parameterize them into two one-dimensional signals. Secondly, use the method of EMD to filter and remove the high-frequency noise of each one-dimensional signal. Finally, obtain the smoothing curve by combining these two processed one-dimensional signals. Meanwhile, in order to eliminate the boundary effect caused of the process of EMD, the method of symmetric extension of endpoints is proposed. The results of experiment show that the new method is effective while smoothing the bivariate discrete plane curve.