To solve the problem whether a nonlinear hyperchaotic system with only one equilibrium point can generate multi-scroll attractors, a new 4D hyperchaotic smooth system with one nonlinear term and a unique equilibrium point is proposed. Based on the 3D Jerk chaotic system constructed by Sprott, the complex dynamic properties of the new system are analyzed and discussed theoretically by using the Routh-Hurwitz criterion, the central manifold theorem and the mathematical simulation software, and by combining with the feedback control technology and the design method of multi-scroll chaotic system. It is found that there is a unique equilibrium point in the system, and the applicable parameters range of this equilibrium point in different states is given. It is strictly proved that the Hopf bifurcation phenomenon exists in the new system, and the Lyapunov exponential spectrum, bifurcation graph and Poincaré mapping of the new system are further obtained by numerical simulation. It is verified that the new system has only one saddle-focus and can produce complex dynamics such as multi-scroll hyperchaotic attractor and periodic attractor, which enriches the research on hyperchaotic complexity of the existing Jerk system.