Automatic modulation classification (AMC) is an essential and meaningful technology in the development of cognitive radio. It can judge the modulation mode according to the signal acquired by the receiver. In recent years, the deep learning (DL) method has been used to take the place of modulation signal recognition based on decision theory and pattern recognition, which has achieved very effective results. The development of the neural network classification model focuses on architectural engineering. Discovering state-of-the-art neural network architectures requires substantial prior knowledge and effort of human experts. Neural architecture search (NAS) can be viewed as a subdomain of automatic machine learning (AutoML), which uses a neural network to automatically adjust the structures and parameters to obtain a network that researchers need by following search strategies that maximize performance. In this paper, we propose a differentiable architecture search (DARTS) based AMC method. In addition, we also consider six other methods, including convolutional neural network (CNN), simple recurrent unit (SRU), a convolutional-recurrent neural network (CRFN-CSS), Residual Networks (ResNet), Inception Modules (Inception) and MobileNet. Simulation results show that the proposed method can achieve the optimal classification accuracy at low parameters and floating-point operations (FLOPs) without manual architecture engineering.