Recently, deep learning methods based on three-dimensional (3-D) convolution have been widely used in the hyperspectral image (HSI) classification tasks and shown good classification performance. However, affected by the irregular distribution of various classes in HSI datasets, most previous 3-D convolutional neural network (CNN)-based models require more training samples to obtain better classification accuracies. In addition, as the network deepens, which leads to the spatial resolution of feature maps gradually decreasing, much useful information may be lost during the training process. Therefore, how to ensure efficient network training is key to the HSI classification tasks. To address the issue mentioned above, in this paper, we proposed a 3-DCNN-based residual group channel and space attention network (RGCSA) for HSI classification. Firstly, the proposed bottom-up top-down attention structure with the residual connection can improve network training efficiency by optimizing channel-wise and spatial-wise features throughout the whole training process. Secondly, the proposed residual group channel-wise attention module can reduce the possibility of losing useful information, and the novel spatial-wise attention module can extract context information to strengthen the spatial features. Furthermore, our proposed RGCSA network only needs few training samples to achieve higher classification accuracies than previous 3-D-CNN-based networks. The experimental results on three commonly used HSI datasets demonstrate the superiority of our proposed network based on the attention mechanism and the effectiveness of the proposed channel-wise and spatial-wise attention modules for HSI classification. The code and configurations are released at Github.com.