A novel technique to achieve real-time and high-precision interrogation of a linearly chirped fiber Bragg (LCFBG) grating sensor array based on dispersive time delay and optical pulse compression is proposed and experimentally demonstrated. In the proposed system, an ultra-short optical pulse is launched into an LCFBG sensor array consisting of N identical LCFBGs, to produce N reflected pulses with their time delay changes corresponding to the strain or temperature changes. The reflected pulses are sent to another LCFBG having an opposite dispersion coefficient to achieve optical pulse compression to improve the measurement accuracy. A proof-of-concept experiment is demonstrated. A 2×3 LCFBG sensor array using six identical LCFBGs is implemented, and the performance is evaluated experimentally. The sensing speed can be as high as 48.6 MHz, and the sensing accuracy can be as high as 0.26 με for strain and 0.045°C for temperature.