In 1961, Renyi introduced the concept of parametric family of entropies as a generalization of the Shannon entropy. A significant application of this measure can be found in ecology, statistics and various other areas. Later, a divergence measure based on the Renyi entropy was introduced. In this study, we propose a weighted (shift-dependent) version of the Renyi divergence for two doubly truncated nonnegative random variables. Several bounds are obtained. The effect of monotone transformations on the proposed measure is discussed. Finally, a numerical study is performed to provide estimate of the proposed measure. © Springer Nature Switzerland AG 2020.