The phase-matching bandwidth of nonlinear crystal is of great significance in ultrashort laser pulse characterization. In order to satisfy the phase-matching bandwidth, ultra-thin nonlinear crystals are generally required. However, the significantly reduced conversion efficiency, as well as the machining difficulties, limits its applications. Here, we show that sufficient spectrum bandwidth response can be achieved for a thick crystal when the phase-matching wavelength is tuned outside of the spectral window of the measured pulse. By applying this phenomenon to a single-shot second-harmonic generation frequency resolved optical gating (SHG-FROG) device, we successfully characterized a few-cycle pulse using a 150µmβ-barium borate (BBO) crystal. The accuracy of the method was verified by comparing the conventional pulse retrieving approach with a 5µm BBO crystal, which has a sufficient phase-matching bandwidth.