InWireless Sensor Networks (WSNs), exploitation of sink mobility has been considered as a good strategy to balance nodes energy dissipation. Despite of its numerous advantages, data dissemination to mobile sink is a challenging task for resource constrained sensor nodes due to dynamic network topology caused by sink mobility. For efficient data delivery, nodes need to reconstruct their routes towards the latest location of the mobile sink which undermines the energy conservation goal. In this paper, we present a Virtual Grid based Dynamic Routes Adjustment (VGDRA) scheme that aims to minimize the routes reconstruction cost of the sensor nodes while maintaining nearly optimal routes to the latest location of the mobile sink. We propose a set of communication rules that governs the routes reconstruction process thereby requiring only a limited number of nodes to re-adjust their data delivery routes towards the mobile sink. Simulation results demonstrate reduced routes reconstruction cost and improved network lifetime of the VGDRA scheme when compared to existing work.