A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory.