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)(*), increases from about 20 to 200 ps. Moreover, T(2)(*) 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 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 D'yakonov-Perel' and the Bir-Aronov-Pikus mechanisms, with 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.