Automatic modulation classification (AMC) is a signal processing technology used to identify the modulation type of unknown signals without prior information such as modulation parameters for drone communications. In recent years, deep learning (DL) has been widely used in AMC methods due to its powerful feature extraction ability. The significant performance of DL-based AMC methods is highly dependent on large amount of data. However, with the increasingly complex signal environment and the emergence of new signals, several recognition tasks have difficulty obtaining sufficient high-quality signals. To address this problem, we propose an AMC method based on a deep residual neural network with masked modeling (DRMM). Specifically, masked modeling is adopted to improve the performance of a deep neural network with limited signal samples. Both complex-valued and real-valued residual neural networks (ResNet) play an important role in extracting signal features for identification. Several typical experiments are conducted to evaluate our proposed DRMM-based AMC method on the RadioML 2016.10A dataset and a simulated dataset, and comparison experiments with existing AMC methods are also conducted. The simulation results illustrate that our proposed DRMM-based AMC method achieves better performance in the case of limited signal samples with low signal-to-noise ratio (SNR) than other existing methods.