The problem of unknown modulation signal recognition has been received intensely attentions in next-generational intelligent wireless communications. The deep learning (DL) has been widely used in unknown modulation signal recognition due to its excellent performance in solving classification problems and the DL-based automatic modulation classification (AMC) had been proposed. However, DL-based AMC method usually has high space complexity and computational complexity, which limits DL-based AMC to miniaturized devices with limited storage and computing capability. Therefore, a lightweight residual neural network (LResNet) for AMC is proposed in this paper. The simulation results show that the model parameters of LResNet is about 4.8% of the traditional CNN network, and about 14.9% of the ResNet and the classification performance of LResNet improves more than 3% compared with the traditional CNN network and decreases less than 1.5% compared to the ResNet.