The sleep data to be analyzed in clinical treatment are numerous, and it is time-consuming and labor-intensive to distinguish the sleep stages among them. It is essential to classify the sleep stages quickly and accurately by an automatic way. The EEG signals during sleep contain a lot of important low frequency information, and most of the existing convolutional models use large kernel convolution kernels, which are computationally expensive. In this paper, we propose a novel multichannel multi-receptive field Sleep Stage recognition model, MMR-Sleep, which optimally leverages multichannel data by integrating information from multiple perspectives in the time-frequency domain. Specifically, a combination of frequency-aware convolutional neural network (FACNN) and multi-resolutional convolutional neural network (MRCNN) is designed as feature extraction module, which adopts convolutional kernels with different receptive field shapes and sizes to independently extract multi-frequency information from each of the channels in the multichannel data. Further, modern temporal convolutional network (MTCN) processes these features in the time dimension, while the module of multi-head self-attention (MHA) systematically performs channel mixing in the channel dimension to characterize the interdependencies between feature channels. Additionally, to address the convergence challenges inherent in multi-branch networks, we introduce the multi-angle classifier (MAC) module, which allows both branches of FACNN and MRCNN to predict independently, accelerating training while effectively utilizing features acquired by both branches. With extensive experiment results on two public datasets, we demonstrate that the individual modules in MMR-Sleep are effective and can provide more accurate classification performance. The code of MMR-Sleep is available at https://github.com/ddddd222222/MMR-Sleep .