A novel four-dimensiond hyperchaos system with only one nonlinear term is reported. The Lyapunov exponents spectrum, periodic orbit, quasi- periodic orbit, and the chaos and hyperchaos attractor of this system are obtained. A circuit is designed to realize this system by electronic workbench. A synchronization method for the new hyperchaotic systems is established and the mathematical proof of the method is provided. The nonlinear terms in the response system are not dropped. Theoretical analysis and simulation results show that the method is effective.