Theoretical investigation on the group velocity control of ultrafast pulses through quadratic cascading nonlinear interaction is presented. The dependences of the fractional time delay as well as the quality factor of the delayed femtosecond pulse on the peak intensity, group velocity mismatch, wave-vector mismatch and the pulse duration are examined. The results may help to understand to what extent some optical operation parameters could have played a role in controlling the ultrashort pulses. We also predict the maximum achievable pulse delay or advancement efficiency without large distortions. A compact solid medium integrating multiple functions including slowing light, wavelength conversion or broadcasting on a single chip, may bring significant practicality and high integration applications at optical communication band.