Different decay rates are observed by time-resolved pump-probe spectroscopy at different location at the injected electron spin packet, which indicate that spin diffusion exert influence on the measurement of the time constant of electron spin relaxation. The kinetic equation of spin transport is solved. The solution shows that spin diffusion influence electron spin relaxation time by two factors with . One factor relates to the distance between the center of pump spot and the center of probing spot, the other relates to pump spot size. Two conditions under which one may neglect the influence of diffusion are proposed: 1) the center of pump spot and the center of probing spot overlap; 2) pump spot size is large enough. Results show that the more the center of pump spot close to the center of probing spot and the larger pump spot size is, the less spin diffusion influence the measurement of electron spin relaxation time.