A synthetic aperture radar (SAR) target recognition method was proposed based on multivariate empirical mode decomposition (MEMD). MEMD was the general extension of traditional EMD, which could avoid the mode mixing problems. MEMD was employed to process SAR images to obtain the multi-layer intrinsic mode functions (IMF), which could better reflect the time-frequency properties of the targets. Different layers of IMFs could effectively complement each other while sharing some inner correlations because they are generated from the same target. In the classification phase, the joint sparse representation was employed to represent the IMFs. The joint sparse representation could solve several related sparse representation tasks based on the idea of multi-task learning. It could produce more precise estimations than the solutions of single tasks. According to the sparse coefficient vectors corresponding to different IMFs, the reconstruction errors of different classes for the representation of the test sample can be calculated. Afterwards, the target label of the test sample can be determined. Experiments were conducted on the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset, by comparison with existing methods under the standard operating condition, depression angle variance, noise corruption, and target occlusion, the results confirm the validity of the proposed method.