Background: Brain tumor segmentation has a significant impact on the diagnosis and treatment of brain tumors. Accurate brain tumor segmentation remains challenging due to their irregular shapes, vague boundaries, and high variability. Objective: We propose a brain tumor segmentation method that combines deep learning with prior knowledge derived from a region-growing algorithm. Methods: The proposed method utilizes a multi-scale feature fusion (MSFF) module and adaptive attention mechanisms (AAM) to extract multi-scale features and capture global contextual information. To enhance the model's robustness in low-confidence regions, the Monte Carlo Dropout (MC Dropout) strategy is employed for uncertainty estimation. Results: Extensive experiments demonstrate that the proposed method achieves superior performance on Brain Tumor Segmentation (BraTS) datasets, significantly outperforming various state-of-the-art methods. On the BraTS2021 dataset, the test Dice scores are 89.18% for Enhancing Tumor (ET) segmentation, 93.67% for Whole Tumor (WT) segmentation, and 91.23% for Tumor Core (TC) segmentation. On the BraTS2019 validation set, the validation Dice scores are 87.43%, 90.92%, and 90.40% for ET, WT, and TC segmentation, respectively. Ablation studies further confirmed the contribution of each module to segmentation accuracy, indicating that each component played a vital role in overall performance improvement. Conclusion: This study proposed a novel 3D brain tumor segmentation network based on the U-Net architecture. By incorporating the prior knowledge and employing the uncertainty estimation method, the robustness and performance were improved. The code for the proposed method is available at https://github.com/chenzhao2023/UPMAD_Net_BrainSeg.