With the increasing role of oceans and seas in human life, discovering the unexplored underwater regions has become more important in the last decades. The traditional approaches for monitoring underwater environments are not suitable and feasible to human presence, because of the many unpredictable underwater activities, the high water pressure, and the vast volume of unexplored underwater areas. Recently, Underwater Wireless Sensor Networks (UWSNs) have attracted the interest of many researchers as a solution to the exploration of deep sea regions. However, different challenges must be considered when designing and evaluating routing algorithms for these types of networks. These include acoustic communication, continuous node movement and energy consumption. In a previous work, a grid-based routing protocol, called Energy-efficient Multipath Gridbased Geographic Routing (EMGGR), was proposed for UWSN. The proposed algorithm assumes that the monitored region is divided into logical 3D grids. It also assumes that the sensor nodes have identical capabilities and are equipped with localization services. The algorithm consists of three main components: (i) a gateway election algorithm; responsible for electing gateways based on their locations and remaining energy level, (ii) a mechanism for updating neighboring gateways' information; allowing sensor nodes to memorize gateways in local and neighboring cells, and (iii) a packet forwarding mechanism and constructing disjoint paths. Despite its low energy consumption and good packet delivery ratio, EMGGR suffers from high end-to-end delay and high communication overhead. In this work, a multipath disjoint routing scheme based on interconnection networks approach, called Grid Multipath Position-based Routing (GMPR) protocol, which was proposed for MANETs has been adopted for UWSNs. This work has been implemented as a grid-based routing protocol with a Grid Void Avoidance scheme based on GMPR, called Void Avoidance Grid Multipath Position-based Routing (VA-GMPR) protocol. VA-GMPR is able to address the void problem in underwater wireless sensor networks by adopting three mechanisms: hole bypass method, path diversion method and path elimination method. The performance of the proposed protocol has been evaluated via simulation using the AquaSim simulator and compared with the EMGGR protocol. Simulation results show that VAGMPR outperforms EMGGR in terms of packet delivery ratio and average end-to-end delay. However, VA-GMPR consumes more energy than EMGGR.