We have so far developed a fluorescent X-ray computed tomography (FXCT) with a two-dimensional detector based on the pinhole effect for imaging non-radioactive agent distribution in a small animal. However, it takes several hours to acquire a series of projections required for an image with quality sufficient for biological observation. To overcome the difficulty, we realize a high-speed imaging by reducing the number of projections while keeping the image quality using an EM-TV (Expectation Maximization and Total Variation) algorithm, which is a kind of compressed sensing technique. We demonstrate the efficacy by simulation data and actual data obtained in the imaging experiment performed at beamline AR-NE7A, KEK, Tsukuba.