Modulation recognition of single‐component radar signals has been widely studied in the fewer years. Meanwhile, as the electromagnetic environment in the actual battlefields is ever‐increasingly complicated, the demand for the modulation recognition of multi‐component radar signals is also increasing. However, the modulation recognition of single‐component radar signals performs poorly on multi‐component radar signals. To address this problem, a novel modulation recognition method of multi‐component radar signals based on the deep convolutional neural network with a convolutional block attention module (DCNN‐CBAM) is proposed, and the network architecture mainly includes mobile‐inverted bottleneck convolution (MBConv), Fused‐MBConv, and convolutional block attention module (CBAM). An adaptive optimization algorithm Adam with weighted gradient and dynamic bound is proposed for accelerating convergence speed and generalisation performance. The proposed method can not only recognise dual‐component and three‐component radar signals but also four‐component radar signals. The experimental results demonstrate that the recognition accuracies of all radar signals modulation types are more than 83.57% at −8 dB for dual‐component radar signals, 67.41% for three‐component radar signals, and 57.95% for four‐component radar signals, which verify the better recognition performance of DCNN‐CBAM for multi‐component radar signals. The recognition accuracy of the proposed DCNN‐CBAM for dual‐component radar signals can be up to 95.95% at −6 dB, which shows superior recognition performance over the residual method. This work provides an essential guidance for enhancing the recognition performance of multi‐component radar signals.