On the basis of the three-dimensional chaotic system, a new four-dimensional hyperchaotic system is constructed through nonlinear feedback control. An analysis has been made of the stability of the equilibrium point of the system, followed by a further analysis of the dynamic behavior of the system in periodic, chaotic and hyperchaotic states with parameter changes by using phase diagram, bifurcation diagram, Lyapunov exponential spectrum, Poincaré cross-sectional diagram as well as other methods. The numerical solutions of the system can be obtained by adopting finite element method and Runge-Kutta method respectively, accompanied by a comparison between them. Finally, the feasibility of the system can be verified with the designed system analog circuit.