In this paper, the dynamical behaviors of a two-neuron network model with distributed delays and strong kernel are investigated. Considering the mean delay as a bifurcation parameter, explicit algorithms for determining the conditions of Hopf bifurcation are derived. A family of periodic solutions bifurcate from an equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determined in detail by using the theory of normal form and center manifold. Numerical simulations are performed to illustrate the effectiveness of the results found.