In this study, we proposed a new end-to-end convolutional neural network, called MS-SincResNet, for music genre classification. MS-SincResNet appends 1D multi-scale SincNet (MS-SincNet) to 2D ResNet as the first convolutional layer in an attempt to jointly learn 1D kernels and 2D kernels during the training stage. First, an input music signal is divided into a number of fixed-duration (3 seconds in this study) music clips, and the raw waveform of each music clip is fed into 1D MS-SincNet filter learning module to obtain three-channel 2D representations. The learned representations carry rich timbral, harmonic, and percussive characteristics comparing with spectrograms, harmonic spectrograms, percussive spectrograms and Mel-spectrograms. ResNet is then used to extract discriminative embeddings from these 2D representations. The spatial pyramid pooling (SPP) module is further used to enhance the feature discriminability, in terms of both time and frequency aspects, to obtain the classification label of each music clip. Finally, the voting strategy is applied to summarize the classification results from all 3-second music clips. In our experimental results, we demonstrate that the proposed MS-SincResNet outperforms the baseline SincNet and many well-known hand-crafted features. Considering individual 2D representation, MS-SincResNet also yields competitive results with the state-of-the-art methods on the GTZAN dataset and the ISMIR2004 dataset. The code is available at https://github.com/PeiChunChang/MS-SincResNet.