With the wide application of high-resolution radar, the application of Radar Automatic Target Recognition (RATR) is increasingly focused on how to quickly and accurately distinguish high-resolution radar targets. Therefore, Synthetic Aperture Radar (SAR) image recognition technology has become one of the research hotspots in this field. Based on the characteristics of SAR images, a Sparse Data Feature Extraction module (SDFE) has been designed, and a new convolutional neural network SSF-Net has been further proposed based on the SDFE module. Meanwhile, in order to improve processing efficiency, the network adopts three methods to classify targets: three Fully Connected (FC) layers, one Fully Connected (FC) layer, and Global Average Pooling (GAP). Among them, the latter two methods have less parameters and computational cost, and they have better real-time performance. The methods were tested on public datasets SAR-SOC and SAR-EOC-1. The experimental results show that the SSF-Net has relatively better robustness and achieves the highest recognition accuracy of 99.55% and 99.50% on SAR-SOC and SAR-EOC-1, respectively, which is 1% higher than the comparison methods on SAR-EOC-1.