Time-resolved circularly polarized and linearly polarized pump-probe spectroscopies are used to study the recombination dynamics of spin-polarized and spin-nonpolarized electrons as well as its evolution with photon energy for an intrinsic GaAs at 9.6K. It is found that the spin polarization has a significant influence on the electron recombination dynamics. The spectroscopic measurements give the same recombination lifetime only when measured near the bottom of the conduction band, but different recombination lifetimes were measured in higher excess-energy states. It is pointed out that the recombination lifetime measured by circularly polarized pump-probe spectroscopy, rather than that measured by linearly-polarized pump-probe spectroscopy, should be used to solve for the lifetime of electron-spin coherence from time-resolved Faraday spectroscopic data. The theoretical calculation agrees well with the experimental results.