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Fast beam profile measurement is important in fast beam dynamic behavior investigations. A bunch-by-bunch beam size measurement system, which is presently used to measure horizontal profile, has been developed at the Shanghai Synchrotron Radiation Facility(SSRF)and is capable of measuring bunches within a separation of 2 ns. The system is based on a direct-imaging optical system and high-speed photomultiplier array detector. A high-band-width linear signal amplifier and acquisition module have also been designed to process bunch-by-bunch multi-channel signals from the detector.The software resampling technique and principal component analysis method were developed to obtain the synchronized data and enhance the signal-to-noise ratio. The fast injection of transients was successfully captured and analyzed.Moreover,the bunch-by-bunch positions and sizes exhibited strong oscillation after the injection at the horizontal betatron oscillation frequency of the SSRF storage ring,and this demonstrated the bunch-by-bunch measurement capability of our system.