The many-electron effects on the two-dimensional D^- centre in a strong magnetic field are investigated in the framework of a static random-phase and low-wavenumber approximation. It is found that the energy levels of the D^- centre oscillate with Landau filling factor. A decrease in the temperature intensifies the oscillation. The screening of the electron gas on the Coulomb potential can be weakened greatly when the Landau filling factor is an integer. It is also found that the state of total angular momentum L=-2 can be a bound state only when the Landau filling factor is in a certain region centering at an integer and the temperature is low enough.