In the global navigation satellite system (GNSS), identifying not only single but also compound jamming signals is crucial for ensuring reliable navigation and positioning, particularly in future wireless communication scenarios such as the space-air-ground integrated network (SAGIN). However, conventional techniques often struggle with low recognition accuracy and high computational complexity, especially under low jamming-to-noise ratio (JNR) conditions. To overcome the challenge of accurately identifying compound jamming signals embedded within GNSS signals, we propose ACSNet, a novel convolutional neural network designed specifically for this purpose. Unlike conventional methods that tend to exhibit lower accuracy and higher computational demands, particularly in low JNR environments, ACSNet addresses these issues by integrating asymmetric convolution blocks, which improve sensitivity to subtle signal variations while reducing the number of parameters by approximately 50% compared to symmetric convolutional designs. Simulations demonstrate that ACSNet significantly improves accuracy in low JNR regions and shows robust resilience to power ratio (PR) variations. It achieves an overall accuracy of 91.84% and a Kappa coefficient (×100) of 90.82, and notably reaches near 100% recognition accuracy when the JNR is greater than or equal to −9 dB, confirming its effectiveness and efficiency for practical GNSS interference management applications.