This paper is devoted to introducing a new three dimensions hyperchaotic system and adapting it to enhance the Hight algorithm. The proposal hyperchaotic system with one equilibrium point is mainly derived from the Lorenz system, which we called (3D-NSC). The dynamic analysis of 3D-NSC presents some properties such as; stability of symmetric equilibria; phase diagram, bifurcation and Lyapunov exponents (LE), which are all investigated analytically and numerically. Also, the circuit design of the 3D-NSC is introduced with some properties. The proposed system is occupied with improving the Hight algorithm. The main propose system is to create a key schedule for the chaotic Hight algorithm. This system is then applied to encrypt different images types. Our proposed system showed high encryption efficiency compared to systems, based on some performance analyzes such as; histogram, pixel change rate (NPCR), standardized variable mean intensity (UACI), pixel correlation, and entropy.