High-resolution range profile (HRRP) target recognition is an important task in radar signal processing. However, HRRP signals are highly sensitive to target attitude and observation conditions. In addition, available HRRP samples are often limited. Therefore, existing methods usually show limited performance in complex multi-class small-sample HRRP recognition scenarios. In this paper, an efficient convolutional neural network (CNN) architecture is proposed for small-sample HRRP target recognition. Multi-scale convolutional branches are combined with the squeeze-and-excitation (SE) attention mechanism for small-sample HRRP target recognition. Multi-scale temporal features can be captured by the proposed network. Key channel features can also be adaptively enhanced by the SE module. In addition, label smoothing regularization is introduced to improve the generalization ability of the model. Extensive ablation and comparison experiments were conducted on a real HRRP dataset with 11 target classes. The experimental results show that the proposed method achieves the accuracy of 91.81, and significantly outperforms the classical CNN and ResNet1D baseline models. These results demonstrate the effectiveness of the proposed network structure and regularization strategy. It provides a promising solution for small-sample multi-class HRRP target recognition.