Quantitative phase contrast microscopy (QPCM) can realize high-quality imaging of sub-organelles inside live cells without fluorescence labeling, yet it requires at least three phase-shifted intensity images. Herein, we combine a novel convolutional neural network with QPCM to quantitatively obtain the phase distribution of a sample by only using two phase-shifted intensity images. Furthermore, we upgraded the QPCM setup by using a phase-type spatial light modulator (SLM) to record two phase-shifted intensity images in one shot, allowing for real-time quantitative phase imaging of moving samples or dynamic processes. The proposed technique was demonstrated by imaging the fine structures and fast dynamic behaviors of sub-organelles inside live COS7 cells and 3T3 cells, including mitochondria and lipid droplets, with a lateral spatial resolution of 245 nm and an imaging speed of 250 frames per second (FPS). We imagine that the proposed technique can provide an effective way for the high spatiotemporal resolution, high contrast, and label-free dynamic imaging of living cells.