The temporal and spectral evolutions of the fundamental and second harmonic (SH) pulses were simulated in the propagation. By introducing the walk-off length and nonlinear length, the walk-off effect, group-velocity dispersion and cubic nonlinearity were described. The wavelength tuning characteristics of femtosecond-pulse second harmonic generation (SHG) were analyzed. It was found that the full width at half maximum (FWHM) of the SHG wavelength tuning curve of 40 fs pump pulses can reach as wide as 42 nm, while that of 40 ps pump pulses is only 2.8 nm.