In the chaos literature, there is great interest in the modelling of hyperchaotic systems as they have high complexity. This paper announces a new 4-D hyperchaotic system with a two-scroll attractor. The phase portraits and qualitative properties of the new hyperchaotic system are explored with MATLAB plots, bifurcation diagram, Lyapunov exponents, Kaplan-Yorke dimension, etc. The hyperchaotic system has a unique saddle-point equilibrium at the origin. As a control application, the adaptive stabilization of the new hyperchaotic system is detailed using Lyapunov stability theory. Finally, an electronic circuit of the new hyperchaotic system with MultiSIM is designed and a good match between the plots of the theoretical model and the circuit model is obtained for the new hyperchaotic system with two-scroll attractor.