The Transformer architecture has gained widespread acceptance in image segmentation. However, it sacrifices local feature details and necessitates extensive data for training, posing challenges to its integration into computer-aided medical image segmentation. To address the above challenges, we introduce CCFNet, a collaborative cross-fusion network, which continuously fuses a CNN and Transformer interactively to exploit context dependencies. In particular, when integrating CNN features into Transformer, the correlations between local and global tokens are adaptively fused through collaborative self-attention fusion to minimize the semantic disparity between these two types of features. When integrating Transformer features into the CNN, it uses the spatial feature injector to reduce the spatial information gap between features due to the asymmetry of the extracted features. In addition, CCFNet implements the parallel operation of Transformer and the CNN and independently encodes hierarchical global and local representations when effectively aggregating different features, which can preserve global representations and local features. The experimental findings from two public medical image segmentation datasets reveal that our approach exhibits competitive performance in comparison to current state-of-the-art methods.