We study and experimentally demonstrate a sensitive single-shot correlation system in which only a diffraction grating is used to produce a transverse time delay (TTD) in the reference pulse. The mechanism of the TTD introduced by the grating and the formation of the relative time delay (RTD) in the noncollinear correlation system are analyzed in detail. By using our system, we successfully measured the temporal duration of picosecond laser pulses, and a time resolution of ～0.047 ps is obtained at 1047 nm. The impact of the grating dispersion and the second harmonic beam walk-off effect on the measurement are considered.