Under the influence of loss, dispersion, and self-phase modulation, the second-order correlation function of spontaneous Raman scattering photon is calculated by piecewise analysis, and the time mode characteristics of spontaneous Raman scattering pumped by pulsed light in long optical fiber are studied. The results show that in the case of no dispersion and self-phase modulation, the second-order correlation function of spontaneous Raman scattering photon is not affected by pump loss, but is only determined by the ratio of pump pulse width to Raman photon coherence time. It has the same expression as the second-order correlation function of spontaneous parametric downconversion photons. In the case of dispersion and self-phase modulation, the change of pump pulse width caused by dispersion and self-phase modulation and the dispersion-induced temporal wall-off between pump light and Raman photons change the time mode of Raman photons. The second-order correlation function of spontaneous Raman scattering photons depends on the fiber loss coefficient, dispersion parameters and initial pump pulse width, which is no longer the same as that of spontaneous parametric down conversion photons.