A new three-dimensional continuous autonomous chaotic system with a compound power function is constructed. The equation of state of the system has only five terms, one of which is a compound power function with an exponent less than 1. The system has properties of simple structure, non-hyperbolic equilibrium point, coexistence of attractors, and exhibits complex dynamic behaviors. Firstly, dynamic behaviors including Lyapunov exponential spectrum, bifurcation diagram and Poincaré mapping are analyzed. It shows that the system has chaotic characteristics. Then, circuit design of the chaotic system is carried out. Circuit simulation results verify the theoretical analysis.