In view of the realization of a chaotic system circuit, based on the three-dimensional Lü system, a new four-dimensional dynamic hyperchaotic system, with the state variable feedback incorporated, has thus been constructed by adopting the state variable feedback method, followed by a basic dynamic analysis to be carried out. That is, the stability of the equilibrium point is judged by calculating the corresponding eigenvalues according to the Jacobian matrix in consistence with the equilibrium point, with a qualitative analysis to be carried out by using the method of phase space volume ratio to study the dissipation of the system; by calculating the Lyapunov exponent and dimension, and drawing a Poincaré cross-section diagram, etc., a numerical simulation and quantitative analysis of the system are to be carried out as well. Finally, the circuit model of the new hyperchaotic system is built through the basic operational amplifier circuit, thus verifying the accuracy of the circuit realization by Matlab-Simulink.