The dispersion properties of nanofibers was numerically simulated and caculated in details, and different dispersion properties in different diameters and materials were compared. The results show that, there are two zero dispersion wavelengths in nanofibers with silica core. With the increase of fiber diameter, the disperison curve tends to smooth and the zero dispersion wavelength also changes. When the core is silicon, it only have one zero dispersion wavelength. With the increase of diameter, its zero dispersion wavelength moves to the long-wavelength end. The generalized nonlinear Schrdinger equation is adopted to describe the evolution of ultra-short laser pulse propagating in nanofibers, and is solved by using the split-step Fourier method. The influence of dispersion on the generation of supercontinuum and the evolution of pulse profile in different dispersion regions are compared. In the normal dispersion region, the output spectral width is narrow. While in the zero dispersion region and the anomalous dispersion region, the super continuum spectrum can be obtained easily.