In order to realize precise diagnostics for pico-second pulse of peta-watt laser, an auto-correlator especially for single shot pico-second pulse is developed. Optical elements with no dispersion are used in this pico-second auto-correlator′s design, which could improve its precise. Three methods are adopted to testify its characters. Self-calibration is used for time resolution. Over-range is used for time range. Limitation is used for impulse response function. Experiments results show that its time resolution is 0.1 ps/pixel, its time range is 26 ps, and its impulse response function value is 300 fs. So this auto-correlator can fulfill the requirement of precised measurement on pulse width for chirped pulse of pico-second peta-watt laser.