This paper examinesthe behavior of a 4D Lorenz?type hyperchaotic system. First, on the aspect of local dynamics,based on the averaging theory, the Zero?Zero?Hopf bifurcation at the origin of this system is investigated. The parameter conditions of Zero?Zero?Hopf bifurcation are obtained, the existence of two periodic orbits is proved, and their stability is given. Furthermore,on the aspect of global dynamics, by choosing proper parameters and,with the help of numerical simulation,several alternative coexisting attractors of this new hyperchaotic system can be observed, such as hyperchaotic and periodic attractors, different periodic attractors, et al.