Optical time-stretch microscopy has recently attracted intensive attention for its capability of acquiring images at an ultrahigh frame rate. Unfortunately, its achievable frame rate is limited by the requirement of having no overlap between consecutive frames, which leads to a tradeoff between the frame rate (pulse repetition rate) and the amount of the temporal dispersion used for optical image serialization. In this paper, we demonstrate compressive sensing on the platform of optical time-stretch microscopy to overcome the tradeoff between frame rate and temporal dispersion (time stretch) and achieve 50 times higher frame rate than conventional optical time-stretch microscopy. Specifically, we computationally perform compressed optical time-stretch microscopy with an experimental dataset acquired by conventional optical time-stretch microscopy and demonstrate its effects in terms of spatial resolution and cell classification accuracy. Our results indicate that the spatial resolution and cell classification accuracy reach 780 nm and 95% at a line scan rate of 675 MHz and 6.75 GHz, respectively, which correspond to five times and 50 times higher frame rates than what conventional optical time-stretch microscopy can achieve with the same dispersion amount and digitizer sampling rate.