For the first time to our knowledge, it is put forward that GNSE can be resolved by adaptive split-step Fourier method (ASSFM) basing on split-step Fourier method (SSFM) in this paper. It is found that ASSFM must be used to resolve GNSE f or ensuring precision when the frequency shift corresponding to soliton peak val ue is remarkable and microstructure fibers' parameters change along with frequen cy remarkably. It is found that the influence of dispersion on laser pulses evol ution and supercontinuum generation in microstructure fiber is remarkably. Mech anism and scope of expanded spectrum are different in fiber different dispersion regions. The precision of numerical simulation by ASSFM is higher than SSFM in the process of laser pulses propagating in microstructure fibers by reason that the variation of wavelength corresponding to pulse peak power can be considered adequately.