Abstract: Robinson et al studied a class of reduced EEG model, which was discussed with aim to understand its bifurcation character. Considering the time delay of information transmission between the excitatory and inhibitory neuronal population, the effect of time delay on the stability of the reduced model was studied, as well as the conditions under which the Hopf bifurcation occurs. The results showed that the reduced model can keep up its stability when time delay is restricted within a certain threshold. Furthermore, a derivative feedback controller was designed to eliminate the Hopf bifurcation. Numerical simulation verified theoretically the effectiveness of the conclusions as above.