Hyperchaos has important applications in many branches of science and engineering. In this work, we propose a new 4-D hyperchaotic system with three quadratic nonlinearities by modifying the dynamics of hyperchaotic Wang system (Wang et al. 2010). The proposed new hyperchaotic system has a unique equilibrium at the origin, which is a saddle point and unstable. Thus, the new hyperchaotic system exhibits self-excited hyperchaotic attractor. We describe qualitative properties of the new hyperchaotic system such as symmetry, Lyapunov exponents, Kaplan-Yorke dimension, etc. Furthermore, an active control method is derived for the synchronization of two identical new hyperchaotic systems. The circuit experimental results of the new hyperchaotic system show agreement with the numerical simulations.