This paper reports a new three-dimensional （3D）chaotic system with four parameters and three quadratic nonlinearities based on conjugate Lorenz system by feedback control techniques， and tries to investigate complex dynamical behaviors of the new 3D chaotic system. Moreover， dissipativity and equilibria including stability of hyperbolic and nonhyperbolic equilibria are theoretically studied by center manifold theory. Furthermore，the existence of chaotic attractor and periodic attractor is numerically verified through phase portrait， Lyapunov exponents and bifurcation.