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In the task of communication signal recognition, to improve the limitation and low accuracy under the condition of low signal-to-noise ratio (SNR) which used the traditional manual extraction of expert feature, a new method of automatic modulation recognition based on complex baseband signals and convolutional neural network is proposed. In this method, the received signals are preprocessed to obtain the complex baseband signal containing In-Phase components and Quadrature components. The complex baseband signal is input to convolutional neural network model as data set, which trains the convolutional neural network model for many times and adjusts the model structure, filter size, stride, feature map, activation function and other super parameters. The trained convolutional neural network model is used to extract the features and classify signals. The classification and recognition of seven kinds of digital communication signals including 2FSK, 4FSK, BPSK, 8PSK, QPSK, QAM16 and QAM64 are realized. The experimental results show that when the SNR is 0db, the average recognition accuracy of seven types of signals can reach 94.61%, which proves that the algorithm is effective and has high accuracy under the condition of low SNR.