The emergence of convolutional neural network (CNN) has greatly promoted the development of hyperspectral image (HSI) classification technology. However, the acquisition of HSI is difficult. Lack of training samples is the primary cause of low classification performance. Traditional CNN-based methods mainly use 2D CNN for feature extraction, which make interband correlations of HSIs underutilized. 3D CNN extracts the joint-spectral-spatial information representation, but it depends on a more complex model. Also, too deep or too shallow network cannot extract the image features well. To tackle these issues, we propose an HSI classification method based on 2D-3D CNN and multi-branch feature fusion. We first combine 2D CNN and 3D CNN to extract image features. Then, by means of the multi-branch neural network, three kinds of features from shallow to deep are extracted and fused in the spectral dimension. Finally, the fused features are passed into several fully connected layers and a softmax layer to obtain the classification results. In addition, our network model utilizes the state-of-the-art activation function Mish to further improve the classification performance. Our experimental results, conducted on four widely used HSI data sets, indicate that the proposed method achieves better performance than the existing alternatives.