Time-resolved circularly polarized pump–probe spectroscopy is used to study the carrier-density dependence of the electron-spin polarization and spin relaxation dynamics in bulk intrinsic GaAs near the bottom of the conduction band. The experimental result shows that the initial degree of the electron-spin polarization is less than 0.5, and both the initial degree of spin polarization and the spin relaxation time decrease with increasing carrier densities. The simulation calculation shows that the band-gap renormalization effect has a significant influence on the initial degree of spin polarization, but it is not the physical origin of the decrease in the electron-spin polarization. Contrarily, the initial degree of spin polarization can be greatly enhanced by the band-gap renormalization effect for carrier densities above 3.5 × 1017 cm−3. In intrinsic GaAs, both the D'yakonov–Perel' and the Bir–Aronov–Pikus mechanisms play an important role. The Bir–Aronov–Pikus mechanism becomes stronger with the increase in the carrier density, and becomes dominant at high carrier density.