We would like to state well-known Ostrowski inequality via the h-convex function by using the SVN-Reimann integrals. In addition, we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are h-convex functions by using different techniques including Holder’s inequality and power mean inequality. We are introducing very first time that the class of h-convex function, which is the generalization of many important classes including the class of Godunova-Levin s-convex, s-convex in the 2nd kind and hence contains the class of convex functions. It also contains the class of P-convex functions and a class of Godunova-Levin functions. In this way, we also capture the results with respect to the convexity of functions.