A large anisotropy in the spin dephasing times for the different in-plane directions of [0 0 1] quantum wells has been predicted in calculations by Averkiev and Golub [Phys. Rev. B 60 (1999) 15582] for systems with both Rashba and Dresselhaus spin-orbit fields. Here, we present time-resolved Faraday rotation measurements performed in the Voigt geometry on a high-mobility 2D electron system grown on a [0 0 1] substrate. An out-of-plane spin polarization is created in the sample by a circularly polarized pump pulse. The magnetic field applied in the sample plane forces the spins to precess perpendicular to it. For a magnetic field applied along [1 1 0], the spins precess into the View the MathML source direction, which is in the sample plane, for a magnetic field along View the MathML source, the spins precess into the [1 1 0] direction. The experimentally determined spin dephasing times for these two different cases differ by about 60%, demonstrating that the predicted anisotropy is present in our sample.