Quantitative phase contrast microscopy facilitates high-contrast and quantitative phase imaging of transparent samples, eliminating the need for fluorescent labeling, making it pivotal for observing dynamic processes in living cells. Traditional methods, however, require three phase-shifted interferograms to generate a quantitative phase image, resulting in time-intensive procedures. This study introduces a novel phase reconstruction approach for quantitative phase contrast microscopy, leveraging a two-channel convolutional neural network. This innovative method achieves quantitative phase image retrieval from only two phase-shifted interferograms, enhancing imaging speed by 1.5 times and reconstruction speed by an order of magnitude compared with traditional approaches. In our experimental setup, the network was trained using COS7 cell data. The trained network successfully reconstructed quantitative phase images of 3T3 cells, demonstrating its applicability for accurate and robust phase reconstruction across different cell types. This method holds promise as a powerful tool for real-time, high-resolution observation of dynamic living cells and the interaction networks of sub-cellular organelles.