A new fully differential sample-and-hold circuit which can effectively compensate the offset voltage of an operational amplifier and the charge injection of a MOS switch is presented. The proposed circuit shows a true sample-and-hold function without a reset period or an input-track period. The prototype fabricated using a 1.2$mu$m double-polysilicon CMOS process occupies an area of 550$mu$m$ imes$288$mu$m and the error of the sampled ouput is 0.056% on average for 3V input at DC.