In a complex electromagnetic environment, communication signals and interference overlap in the time-frequency domain, and they are difficult to be separated. To solve this problem, a method of interference suppression and communication signal reconstruction based on signal sparse representation is proposed. Firstly, the K-Singular Value Decomposition (K-SVD) algorithm is used to construct the over-complete sub-dictionaries of communication signals and interferences. Then, we build a joint dictionary by over-complete sub-dictionaries, and use the Orthogonal Matching Pursuit (OMP) algorithm to separate and reconstruct the signals. Finally, we simulate the interference suppression and reconstruction process of time-frequency overlapping 2ASK signal and 2PSK signal by computer, and verify the process of interference suppression and signal reconstruction of OFDM signal by experiments. The simulation experimental results show that this method can realize the interference suppression and signal reconstruction of communication signals under the condition of time-frequency overlapping.