Automatic modulation classification (AMC) of received unknown signals is critical in modern communication systems, enabling intelligent signal interception and spectrum management. In this paper, we propose a wavelet-based spectrum convolutional neural network (WS-CNN) model that integrates signal processing techniques with deep learning to achieve robust classification under challenging conditions, including noise, fading, and Doppler effects. The WS-CNN model is based on wavelet analysis and a convolutional neural network (CNN). Specifically, the proposed wavelet analysis, including wavelet threshold denoising, median filtering, and continuous wavelet transformation, is used for signal preprocessing to extract features and generate a compact 2D diagram. The 2D diagram is subsequently fed into the CNN for classification. The simulation results show that the proposed WS-CNN model achieves higher classification rates across a wide range of signal-to-noise ratios (SNRs) compared with existing methods.