Objective: Both local and global context information is crucial semantic features for brain tumor segmentation, while almost all the CNN-based methods cannot learn global spatial dependencies very well due to the limitation of convolution operations. The purpose of this paper is to build a new framework to make full use of local and global features from multimodal MR images for improving the performance of brain tumor segmentation. Approach: A new automated segmentation method named nnUnetFormer was proposed based on nnUnet and transformer. It fused transformer modules into the deeper layers of the nnUnet framework to efficiently obtain both local and global features of lesion regions from multimodal MR images. Main results. We evaluated our method on BraTS 2021 dataset by 5-fold cross-validation and achieved excellent performance with Dice similarity coefficient (DSC) 0.936, 0.921 and 0.872, and 95th percentile of Hausdorff distance (HD95) 3.96, 4.57 and 10.45 for the regions of whole tumor (WT), tumor core (TC), and enhancing tumor (ET), respectively, which outperformed recent state-of-the-art methods in terms of both average DSC and average HD95. Besides, ablation experiments showed that fusing transformer into our modified nnUnet framework improves the performance of brain tumor segmentation, especially for the TC region. Moreover, for validating the generalization capacity of our method, we further conducted experiments on FeTS 2021 dataset and achieved satisfactory segmentation performance on 11 unseen institutions with DSC 0.912, 0.872 and 0.759, and HD95 6.16, 8.81 and 38.50 for the regions of WT, TC, and ET, respectively. Significance: Extensive qualitative and quantitative experimental results demonstrated that the proposed method has competitive performance against the state-of-the-art methods, indicating its interest for clinical applications.