As electromagnetic environments in battlefields are more and more complex, there are more kinds of suppression jamming noise including both single jamming signals and compound jamming signals. Thus, suppression jamming recognition especially for compound jamming signals is becoming vital and challenging. Whereas conventional methods are prone to owning the low recognition accuracy and the high computational complexity, especially under low jamming-to-noise ratio (JNR) conditions. In this paper, a novel jamming recognition network (JRNet) based on robust power-spectrum features is proposed to recognize ten kinds of suppression jamming signals including four single jamming patterns and six compound jamming patterns. The proposed method combines the significant representative power of the JRNet and distinguished power-spectrum features of jamming signals to promote the recognition performance. By integrating residual blocks and asymmetric convolution blocks, the JRNet is capable to address the degradation problem and enhance the recognition ability for subtle features. The simulation results show that the overall recognition accuracy of the proposed method is more than 90% even when the JNR is −18 dB and is close to 100% at −6 dB. Compared with five comparison methods in recent literatures, the proposed JRNet achieves better and stable recognition performance especially under low JNR conditions with relatively less storage source and a bit more FLOPs and inference time.