Automatic modulation recognition (AMR) plays a critical role in modern communication systems. Owing to the recent advancements of deep learning (DL) techniques, the application of DL has been widely studied in AMR, and a large number of DL-AMR algorithms with high recognition rates have been developed. Most DL-AMR algorithm models have high recognition accuracy but have numerous parameters and are huge, complex models, which make them hard to deploy on resource-constrained platforms, such as satellite platforms. Some lightweight and low-complexity DL-AMR algorithm models also struggle to meet the accuracy requirements. Based on this, this paper proposes a lightweight and high-recognition-rate DL-AMR algorithm model called Lightweight Densely Connected Convolutional Network (DenseNet) Long Short-Term Memory network (LDLSTM). The model cascade of DenseNet and LSTM can achieve the same recognition accuracy as other advanced DL-AMR algorithms, but the parameter volume is only 1/12 that of these algorithms. Thus, it is advantageous to deploy LDLSTM in resource-constrained systems.