Frequency-doubling in refractive-index-linear-modulating crystals was investigated numerically. In the case of depleted-pump, changes of conversion efficiency and pulse width with crystal length and band width of phase matching were studied. With the increase of pump pulses energy, pulses are broadened resulted from the unbalanced conversion of fundamental pulses at the different position of the crystal. Due to the modulation of refractive index, there are periodic oscillations in conversion efficiency and pulse width. Subsequently, by analyzing the chirp in harmonic waves, it was found that with the increase of crystal length, the normalized chirp coefficient increase first then decrease and finally tend to 1. The maximum of the normalized chirp coefficient is governed by modulated bandwidth and intrinsic bandwidth. Finally, the effects of phase mismatching parameter on conversion efficiency and pulse width was discussed and the results showed that phase mismatching parameter y determines the location of phasing matching of central frequency. When y=0 is considered, central frequency reaches phase matching at the middle of crystals where is beneficial to improve conversion efficiency and pulse quality.