Jamming is a big threat to the survival of a radar system. Therefore, the recognition of radar jamming signal type is a part of radar countermeasure. Recently, convolutional neural networks (CNNs) have shown their effectiveness in radar signal processing, including jamming signal recognition. However, most of existing CNN methods do not regard radar jamming as a complex value signal. In this study, a complex-valued CNN (CV-CNN) is investigated to fully explore the inherent characteristics of a radar jamming signal, and we find that we can obtain better recognition accuracy using this method compared with a real-valued CNN (RV-CNN). CV-CNNs contain more parameters, which need more inference time. To reduce the parameter redundancy and speed up the recognition time, a fast CV-CNN (F-CV-CNN), which is based on pruning, is proposed for radar jamming signal fast recognition. The experimental results show that the CV-CNN and F-CV-CNN methods obtain good recognition performance in terms of accuracy and speed. The proposed methods open a new window for future research, which shows a huge potential of CV-CNN-based methods for radar signal processing.