BiU-net

•The proposed novel network for medical image segmentation outperforms some SOTA models on four datasets.•Dual-branch encoder effectively captures the local features and models long-distance dependencies.•Two-stage fusion strategy adaptively integrates the features from CNNs and transformers.•The designed context-aware block contains powerful multi-scale feature extraction ability. The proposed novel network for medical image segmentation outperforms some SOTA models on four datasets. Dual-branch encoder effectively captures the local features and models long-distance dependencies. Two-stage fusion strategy adaptively integrates the features from CNNs and transformers. The designed context-aware block contains powerful multi-scale feature extraction ability.