We have studied the spin dynamics of a high-mobility two-dimensional electron system in a GaAs/Al_{0.3}Ga_{0.7}As single quantum well by time-resolved Faraday rotation and time-resolved Kerr rotation in dependence on the initial degree of spin polarization, P, of the electrons. By increasing the initial spin polarization from the low-P regime to a significant P of several percent, we find that the spin dephasing time, $T_2^ast$, increases from about 20 ps to 200 ps; Moreover, $T_2^ast$ increases with temperature at small spin polarization but decreases with temperature at large spin polarization. All these features are in good agreement with theoretical predictions by Weng and Wu [Phys. Rev. B {bf 68}, 075312 (2003)]. Measurements as a function of spin polarization at fixed electron density are performed to further confirm the theory. A fully microscopic calculation is performed by setting up and numerically solving the kinetic spin Bloch equations, including the Dyakonov-Perel and the Bir-Aronov-Pikus mechanisms, with {em all} the scattering explicitly included. We reproduce all principal features of the experiments, i.e., a dramatic decrease of spin dephasing with increasing $P$ and the temperature dependences at different spin polarizations.
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