A spin-1/2 Anderson impurity in a semiconductor quantum well with Rashba and Dresselhaus spin-orbit couplings is studied by using a variational wavefunction method.The local magnetic moment is found to be quenched at low temperatures.The spin-spin correlations of the impurity and the conduction electron density show anisotropy in both spatial and spin spaces,which interpolates the Kondo spin screenings of a conventional metal and of a surface of three-dimensional topological insulators.