Recognizing scenes from synthetic aperture radar (SAR) images has been a challenging task due to the increasing resolution of SAR data. Extracting discriminative features from SAR images is extremely difficult for their sensitivity to target aspect. Considering the intractability of the available deep neural networks in practical implementations, in this brief, we propose a simple and efficient deep sparse tensor filtering network (DSTFN) for SAR image classification. An SAR image is first organized into a data tensor by an overlapped partition. Then, a set of dimension-inseparable geometric filters is developed from a least squares support vector machine, followed by a learned sparse filtering of tensors. Finally, the constructed sparse tensor filters are cascaded to a deep network to automatically extract the discriminative features of the image for accurate classification. Simulations are carried out to verify the effectiveness of the proposed DSTFN.