A new method for compressing ultra-short laser pulse has been proposed in which cascaded quadratic nonlinearity with tilt pulse is used. The pulse compression scheme with group velocity matching between fundamental harmonic (FH) and second harmonic (SH) pulses in a single BBO crystal has been analyzed theoretically. The compressed results have been investigated and compared between the cases of group velocity matching and mismatching. Furthermore, the influences of the phase mismatching between the FH and SH pulses, the length of the nonlinear crystal, the initial peak intensity and pulse-duration of the FH pulse on the pulse-duration compression have been analyzed and simulated. The results show that the matched group velocity between FH and SH pulses can improve significantly both the temporal profile and the spectrum distribution of the compressed pulse. High quality compression can be achieved by optimizing and selecting the parameters such as phase mismatch, length of the nonlinear crystal, initial intensity and so on. For the fundamental pulse with 800 nm central wavelength, 100 fs duration and 50 GW/cm2 peak intensity, the 20fs output FH pulse has been achieved, and at the same time the 14 fs SH pulse has also been generated in 25 mm-long BBO crystal with Δk=60 mm-1 (1.98° detuning angle) and external tilt angle γ0=74°.