Summary: In this paper, we generalize the operator version of Jensen's inequality and the converse one for the class of \(h\)-convex functions. We extend the Hermite-Hadamard's type inequality and a multiple operator version of Jensen's inequality for this class of functions. We also provide a refinement of Jensen's inequality for convex functions. In particular, the operator \(h\) convexity can be reduced to usual \(h\)-convexity in some sense and some results for the other classes of functions can be deduced by choosing an appropriate function \(h\). The superiority of our results is that our results can recover some known results.