We report a novel fourdimensional (4D) hyperchaotic system with a unique equilibrium or two equilibria based on 3D Lorenztype system,and can clearly observe hyperchaotic attractors at each type of equilibria. By utilizing proper Lyapunov function and analytical method,we rigorously prove the nonexistence of homoclinic orbit and heteclinic orbit, further, the hyperchaos of system is no chaos in the sense of Shil’nikov. Further, the ultimate bound sets of system are constructed by Lyapunov function and appropriate optimization. Moreover, the results are verified by numerical simulation method. The complex dynamics are exhibited with the changing parameter by phase portrait, Lyapunov exponents spectrum,bifurcation diagram and Poincare mapping analysis system.