In this talk, a new Lorenz-type system is introduced. The Lyapunov characteristic exponential of this system indicates that this system should have chaotic phenomenon. Numerical simulation illustrates this result which motivates us to further investigate its complex dynamical behaviors. The dynamical entities of its equilibria, such as the stability of the hyperbolic equilibria, the stability for the non-hyperbolic equilibrium, the degenerate pitchfork bifurcation, Hopf bifurcations and the local expressions of stable and unstable manifolds, etc, are first investigated in detail when the parameters are varied in the space of parameters. The existence or non-existence of homoclinic and heteroclinic orbits of this system is then rigorously proved.