Convolutional neural networks (CNNs) have gained tremendous success in solving complex inverse problems. The aim of this work is to develop a novel CNN framework to reconstruct video sequences of dynamic live cells captured using a computational microscopy technique, Fourier ptychographic microscopy (FPM). The unique feature of the FPM is its capability to reconstruct images with both wide field-of-view (FOV) and high resolution, i.e. a large space-bandwidth-product (SBP), by taking a series of low resolution intensity images. For live cell imaging, a single FPM frame contains thousands of cell samples with different morphological features. Our idea is to fully exploit the statistical information provided by these large spatial ensembles so as to make predictions in a sequential measurement, without using any additional temporal dataset. Specifically, we show that it is possible to reconstruct high-SBP dynamic cell videos by a CNN trained only on the first FPM dataset captured at the beginning of a time-series experiment. Our CNN approach reconstructs a 12800×10800 pixel phase image using only ∼25 seconds, a 50× speedup compared to the model-based FPM algorithm. In addition, the CNN further reduces the required number of images in each time frame by ∼ 6×. Overall, this significantly improves the imaging throughput by reducing both the acquisition and computational times. The proposed CNN is based on the conditional generative adversarial network (cGAN) framework. We further propose a mixed loss function that combines the standard image domain loss and a weighted Fourier domain loss, which leads to improved reconstruction of the high frequency information. Additionally, we also exploit transfer learning so that our pre-trained CNN can be further optimized to image other cell types. Our technique demonstrates a promising deep learning approach to continuously monitor large live-cell populations over an extended time and gather useful spatial and temporal information with sub-cellular resolution.