This paper presents the results of a feedback technique for controlling low frequency surge oscillations in an axial compressor. To simulate surge a hybrid model is developed, by coupling the Moore - Greitzer potential flow model and the Navier - Stokes solution, to result in more realistic flow predictions. This hybrid model incorporates the viscous effect on the flow behaviour, which is neglected in the Moore - Greitzer model. The present model is shown to capture the existence of rotating stall disturbances in the combustor during a typical classic surge cycle as has been reported in the experiments. After modelling the surge we propose a steady feedback control scheme to minimise the adverse effect of the surge oscillations on the combustor operation. The results for a four hole and six hole feedback control mechanisms are reported and it is seen that the existing high frequency fluctuations in the unsteady variation of plenum pressure before control are virtually eliminated in the presence of a steady feedback control. Due to decrease in the frequency of plenum pressure variations in the presence of feedback control, the variations have now become smoother and are seen to be relatively more stabilised. It is also shown that the steady feedback control is effective in reducing both the hysteresis and the energy loss from the flow thereby the work output from the turbine is expected to improve which in turn can lead to greater cycle efficiency. The present study also reveals that by using six hole feedback mechanism complete recovery from the adverse pressure gradient is possible, but at the expense of a reduced pressure delivery by the compressor. It is expected that the scheme proposed here is relatively simple to implement compared to the many other control schemes available today.