Sufficient training samples are prerequisite for most existing automatic target recognition (ATR) algorithms to obtain satisfactory recognition performance. Nevertheless, sometimes only a few samples are available in real synthetic aperture radar (SAR) application scenarios. Therefore, this paper proposes a Siamese subspace classification network to address the problem of SAR ATR with insufficient training samples. To be specific, the proposed method first establishes a feature embedding network based on Siamese structure, and leverages contrastive learning to train a low-dimensional representation space with both intra-class compactness and inter-class divergence. A subspace learning-based classifier is then designed to reason the identity of the target. Experimental results on moving and stationary target acquisition and recognition (MSTAR) benchmark data set demonstrate the effectiveness and superiority of the proposed method.