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The UNet architecture, based on Convolutional Neural Networks (CNN), has demonstrated its remarkable performance in medical image analysis. However, it faces challenges in capturing long-range dependencies due to the limited receptive fields and inherent bias of convolutional operations. Recently, numerous transformer-based techniques have been incorporated into the UNet architecture to overcome this limitation by effectively capturing global feature correlations. However, the integration of the Transformer modules may result in the loss of local contextual information during the global feature fusion process. To overcome these challenges, we propose a 2D medical image segmentation model called Multi-scale Cross Perceptron Attention Network (MCPA). The MCPA consists of three main components: an encoder, a decoder, and a Cross Perceptron. The Cross Perceptron first captures the local correlations using multiple Multi-scale Cross Perceptron modules, facilitating the fusion of features across scales. The resulting multi-scale feature vectors are then spatially unfolded, concatenated, and fed through a Global Perceptron module to model global dependencies. Furthermore, we introduce a Progressive Dual-branch Structure to address the semantic segmentation of the image involving finer tissue structures. This structure gradually shifts the segmentation focus of MCPA network training from large-scale structural features to more sophisticated pixel-level features. We evaluate our proposed MCPA model on several publicly available medical image datasets from different tasks and devices, including the open large-scale dataset of CT (Synapse), MRI (ACDC), fundus camera (DRIVE, CHASE_DB1, HRF), and OCTA (ROSE). The experimental results show that our MCPA model achieves state-of-the-art performance. The code is available at https://github.com/simonustc/MCPA-for-2D-Medical-Image-Segmentation.