The paper studies the dynamical behaviors of a recurrent neural network model consisting of three neurons with time delays through theoretical analysis and numerical simulations. The local stability of the trivial equilibrium of the network is analyzed and the sufficient conditions of the existence of Hopf bifurcation are given by discussing the associated characteristic equation. The direction and stability of the bifurcated periodic oscillations arising from Hopf bifurcation, which depend on the nonlinear terms of the network, are determined by means of the normal form and the center manifold theorem. Afterwards, numerical examples are performed to validate the theoretical analysis. The case studies of numerical simulations reach nice agreement with the theoretical results.