The phase-matching function and spectral function of spontaneous four-wave mixing in the fiber pumped by picoseconds pulse are derived, to study spectral characteristics of correlated photon pairs at 800 nm based on photon crystal fiber (PCF), The calculation result shows that the optimized spectral symmetry can be achieved by choosing the idler wavelength at 796 nm in the fiber. By using the simplified spectral function, the evolved effects and changing law of the signal light and idle light, were discussed under the condition of the idler light with a single frequency, by changing the dispersion slope at the zero dispersion wavelength, the nonlinear coefficient and the central wavelength of pump pulse. Parameters in favor of high purity photon pairs were presented. These results provide reference for developing entangled photon sources based on photon crystal fiber at 800 nm wave band.