Convolutional neural network(CNN) has achieved great success in optical image recogniton, and has been applied in research of synthetic aperture radar(SAR) automatic target recognition(ATR) recently. However, in real SAR systems, SAR images are usually compressed for transmission due to the limited wireless bandwidth, and few researches have evaluated the influence of image compression on SAR ATR task. In this paper, an efficient CNN architecture based on inception module and batch normalization layer is proposed for SAR ATR tasks, and the impact of image compression on SAR ATR is evaluated based on the proposed model. The experiments are based on MSTAR dataset, and the test images are compressed by Set Partitioning in Hierarchical Trees(SPIHT) algorithm with different compression ratio. Experimental results show that the proposed CNN model achieves a state-of-the-art classification accuracy of 99.29% on original MSTAR dataset, and can still get high classification accuracy above 90% even SAR images in test set are compressed by nearly one hundred times, which reveals that moderate compression of SAR images has little influence on SAR ATR tasks, and this validates the practicability of applying the proposed model to real SAR ATR systems.