Deep neural networks have faced many problems in hyperspectral image classification, including the ineffective utilization of spectral-spatial joint information and the problems of gradient vanishing and overfitting that arise with increasing depth. In order to accelerate the deployment of models on edge devices with strict latency requirements and limited computing power, this paper proposes a learnable group convolution network (LGCNet) based on an improved 3D-DenseNet model and a lightweight model design. The LGCNet module improves the shortcomings of group convolution by introducing a dynamic learning method for the input channels and convolution kernel grouping, enabling flexible grouping structures and generating better representation ability. Through the overall loss and gradient of the backpropagation network, the 3D group convolution is dynamically determined and updated in an end-to-end manner. The learnable number of channels and corresponding grouping can capture different complementary visual features of input images, allowing the CNN to learn richer feature representations. When extracting high-dimensional and redundant hyperspectral data, the 3D convolution kernels also contain a large amount of redundant information. The LGC module allows the 3D-DenseNet to choose channel information with more semantic features, and is very efficient, making it suitable for embedding in any deep neural network for acceleration and efficiency improvements. LGC enables the 3D-CNN to achieve sufficient feature extraction while also meeting speed and computing requirements. Furthermore, LGCNet has achieved progress in inference speed and accuracy, and outperforms mainstream hyperspectral image classification methods on the Indian Pines, Pavia University, and KSC datasets.