The paper presents a new four-dimensional autonomous hyper-chaotic system by introducing a state variable into the three-dimensional autonomous chaotic system based on studying and analyzing some hyper-chaos. Compared with other hyper-chaotic systems，the bigger positive Lyapunov exponent of the new system is bigger, and the range of hyper-chaos is also wider when the parameter varies. Numerical simulations and bifurcation analysis are done in this paper, and an analog electronic circuit is designed to verify the new system. The experiment results show that various attractors of the hyper-chaotic circuit, including periodic attractor, quasi-periodic attractor，chaotic attractor，hyper-chaotic attractor，are well agree with the simulation results.