In the frequency conversion process of ultrashort pulses, due to group-velocity mismatch (GVM), conversion efficiency, crystal length and pulse bandwidth will affect each other and result in low efficiency or small bandwidth. Based on the nonlinear coupling equations, the analytical expressions about group-velocities of fundamental (FH) and second-harmonic (SH) pulses are derived under the plane-wave and pump un-depletion approximations. THG mixing process with ultrashort pulses (FWHM ≈200 fs) input is numerically simulated in type-Ⅱ KDP crystals. The results show that conversion efficiency of 3ω exponentially decrease along with the square of difference between reciprocal of group-velocities of FH and SH pulses, which agree with our theoretical results. Conclusions of this paper are the necessary supplement to the group-velocity-matching relationship of THG, which will be useful for finding proper nonlinear crystals and choosing effective GVM methods in the THG process of ultrashort pulses.