In this paper we have considered a difference of Jensen's inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csiszár \cite{csi1} $f-$divergence. A result is established that allow us to compare two measures under certain conditions. By the application of this result we have obtained a new inequality for the well known means such as arithmetic, geometric and harmonic. Some divergence measures based on these means are also defined.