The transmission of optical signal under the effects of cross-phase modulation (XPM) and self-phase modulation (SPM) together in pump-probe wave structure is investigated in intensity modulation direct detection wavelength division multiplexing (IM-DD WDM) systems. The analytical method to determine the time-domain shape of probe wave when arbitrary wave is inputted in pump channel is confirmed. The impact of channel spacing and transmission rate on XPM is assessed. It is found that the main effect of SPM in pump channel is to increase time-domain intensity-modulation index to a certain extent. The analytical result agrees well with numerical simulation.