A new class of generalized convex functions called sub-$b$-$s$-convex functions is defined by modulating the definitions of $s$-convex functions and sub-$b$-convex functions. Similarly, a new class sub-$b$-$s$-convex sets, which are generalizations of $s$-convex sets and sub-$b$-convex sets, is introduced. Furthermore, some basic properties of sub-b-s-convex functions in both general case and differentiable case are presented. In addition the sufficient conditions of optimality for both unconstrained and inequality constrained programming are established and proved under the sub-$b$-$s$-convexity.