Abstract: A new three-dimensional piecewise-linear chaotic system is proposed. Some dynamical characteristics of this system including symmetry and invariance, dissipativity and existence of attractor, equilibrium, and stability are investigated in detail. By numerical simulating with Lyapunov exponent spectrum, bifurcation diagram, Poincaré mapping, and phase portrait, this paper verifies that the proposed system has abundant dynamical behaviors. It can operate on chaotic and periodic orbits and can evolve into chaos with difform chaotic attractor or period or limited point by a constant controller.