Based on conjugate Lorenz system, a new 4D secondorder hyperchaotic multinomial system with two nonlinear terms is obtained by using feedback control technique. In order to better understand this system, the local dynamic properties of this system including dissipativity, the number and stability of the equilibrium point, Lyapunov dimension and so on are studied, the existence of Hopf bifurcation of this system is proved, and the generating condition of this bifurcation is given. Numerical analysis method including phase portrait, bifurcation diagram, Lyapunov exponents and so on are further used to verify that the complex dynamic property exists in the new system.