Fourier ptychographic microscopy (FPM), as an emerging computational imaging method, has been applied to quantitative phase imaging with resolution bypassing the physical limit of the detection objective. Due to the weak illumination intensity and long image acquisition time, the achieved imaging speed in current FPM methods is still low, making them unsuitable for real-time imaging applications. We propose and demonstrate a high-speed FPM method based on using laser illumination and digital micro-mirror devices for illumination angle scanning. In this new, to the best of our knowledge, FPM method, we realized quantitative phase imaging and intensity imaging at over 42 frames per second (fps) with around 1 µm lateral resolution. The quantitative phase images have revealed membrane height fluctuations of red blood cells with nanometer-scale sensitivity, while the intensity images have resolved subcellular features in stained cancer tissue slices.