Abstract Benefitted from its great success on many tasks, deep learning is increasingly used on low-computational-cost devices, e.g. smartphone, embedded devices, etc. To reduce the high computational and memory cost, in this work, we propose a fully learnable group convolution module (FLGC for short) which is quite efficient and can be embedded into any deep neural networks for acceleration. Specifically, our proposed method automatically learns the group structure in the training stage in a fully end-to-end manner, leading to a better structure than the existing pre-defined, twosteps, or iterative strategies. Moreover, our method can be further combined with depthwise separable convolution, resulting in 5× acceleration than the vanilla Resnet50 on single CPU. An additional advantage is that in our FLGC the number of groups can be set as any value, but not necessarily 2k as in most existing methods, meaning better tradeoff between accuracy and speed. As evaluated in our experiments, our method achieves better performance than existing learnable group convolution and standard group convolution when using the same number of groups.