Based on the dynamical investigation of Lorenz system, the paper analyses the equilibrium bifurcation of the Lorenz-84 system by rigorous mathematical theory and numerically simulates its dynamical behaviors. Firstly, the equilibrium is investigated and the conditions of Hopf bifurcation are obtained; Secondly, its complex dynamic behaviors are analyzed by means of Lyapunov spectrum, bifurcation diagram, phase portraits and Poincaré maps, which verify properties of chaotic attractor of the system. All analysis results express that the system can occur equilibrium bifurcation and exist chaotic states in particular parameter interval.