A time- and space-resolved circularly polarized pump-probe spectroscopy and its theory are developed, and are used experimentally to study electron spin diffusion transport in intrinsic GaAs quantum wells. The ambipolar spin diffusion coefficient of Ｄas=37.5±15 cm2/s is obtained at room temperature, and is smaller than that in a doped GaAs quantum well obtained by spin grating. The difference is explained based on “hole Coulomb drag" effect which slows the diffusion transport of electron spin packet.