In this paper, we propose a Hybrid High-resolution and Non-local Feature Network (H2NF-Net) to segment brain tumor in multimodal MR images. Our H2NF-Net uses the single and cascaded HNF-Nets to segment different brain tumor sub-regions and combines the predictions together as the final segmentation. We trained and evaluated our model on the Multimodal Brain Tumor Segmentation Challenge (BraTS) 2020 dataset. The results on the test set show that the combination of the single and cascaded models achieved average Dice scores of 0.78751, 0.91290, and 0.85461, as well as Hausdorff distances ($95\%$) of 26.57525, 4.18426, and 4.97162 for the enhancing tumor, whole tumor, and tumor core, respectively. Our method won the second place in the BraTS 2020 challenge segmentation task out of nearly 80 participants.