Based on the nonlinear coupling equations，the relation between group-velocities of 1ω，2ω and 3ω waves in the mixing process of broadband third-harmonic generation (THG) is investigated theoretically. The formula of three-wave group-velocity-matching (GVM) is derived. The THG mixing process of ultrashort pulses in Type-Ⅱ KDP crystals is simulated. Obtained results show that both the THG conversion efficiency and the bandwidth reach maximum when the formula is satisfied (i.e., at zero group-velocity mismatch)，and drop down rapidly when it's not satisfied. The three-wave GVM formula presented is useful for finding proper nonlinear crystals and choosing effective GVM methods.