Modulation classification detects the modulation type of received signals to guarantee that the signals can be correctly demodulated and that the transmitted message can be accurately recovered. For the modulation classification of M-PSK, M-QAM and M-APSK modulated signals with similar constellation maps, we analyze waveform characteristics of the signal in the time domain. Based on the waveform characteristics of the signal, we explore the feasibility of using convolutional neural network (CNN) to identify the modulation classification of the signal. We analyze the data input structure and network model required for modulation classification using CNN. Considering the impairment of the signal by additive white Gaussian noise (AWGN), clock offset and Rician multipath fading, a combined channel is simulated in this paper to obtain the impaired data as dataset. The simulation results show that CNN has great potential for modulation classification.