Radar signal recognition is an indispensable part of an electronic countermeasure system. In order to solve the problem that the current techniques have, which is a low recognition rate and a slow recognition speed for radar signals, a rapid accurate recognition system is proposed, especially for when multiple signals arrive at the receiver. The proposed system can recognize eight types of radar signals while separating signals: binary phase shift keying (BPSK), linear frequency modulation (LFM), Costas, Frank code, and P1–P4 codes. Regression variational mode decomposition (RVMD) is explored to separate the received signals, which saves time for parameter optimization of variational mode decomposition (VMD). Furthermore, signal separation and a noise removal technique based on VMD and the first component recognition technique based on a deep belief network (DBN) are proposed. In addition, in order to overcome the loss of the secondary component caused by signal separation, a fusion network is explored to increase the recognition rate of the secondary component in a short time. The simulation results show that the recognition system achieves an overall recognition rate of 99.5% and 94% at a signal-to-noise ratio (SNR) of 0 dB when receiving single signals and double signals, while spending 0.8 s and 2.23 s, respectively. The proposed system can also be used to recognize medical and mechanical signals.