In recent years, deep learning methods have been widely applied in the field of signal processing and have achieved good results. Deep learning methods can automatically acquire useful signal features from massive signal data using neural network models designed by experts, but the manual design of deep neural network models remains a time-consuming and error-prone process. To address this, a method for Automatic Modulation Classification (AMC) based on progressive neural architecture search is proposed. This method can automatically design network structures according to specific modulation classification tasks and obtain the optimal lightweight deep neural network by following a search strategy that maximizes the model performance. Simulation results show that compared to deep learning-based modulation classification methods, the proposed method can achieve optimal modulation classification accuracy without manual design of neural networks, with low parameter volume and floating-point operations, achieving an average recognition accuracy up to 92.82%.