We have investigated the intersubband scattering of electrons in GaAs quantum wells using luminescence up-conversion with 100-fs resolution. The decay time of the n=2 electron-to-heavy-hole transition (e,hh)(2) depends both on the excess energy of the charge carriers and on the excitation density. A Monte Carlo simulation allows us to reproduce the experimental data with high accuracy. The intrinsic LO-phonon scattering rate is found to be 2.0x10(12) s(-1) for 80-meV subband separation. We show the wave-vector dependence and explain the density and excess energy dependence.