This work proposes a geographic routing protocol for UWSNs based on the construction of a 3D virtual grid structure, called Void-Avoidance Grid-based Multipath Position-based Routing (VA-GMPR). It consists of two main components, the multipath routing scheme and the grid-based void avoidance (GVA) mechanism for handling routing holes. The multipath routing scheme adopts node-disjoint routes from the source to the sink in order to enhance network reliability and load balancing. While the GVA mechanism handles the problem of holes in 3D virtual grid structure based on three techniques: Hole bypass, path diversion, and path backtracking. The performance evaluation of the VA-GMPR protocol was compared to a recently proposed grid-based routing protocol for UWSNs, called Energy-efficient Multipath Geographic Grid-based Routing (EMGGR). The results showed that the VA-GMPR protocol outperformed the EMGGR protocol in terms of packet delivery ratio, and end-to end-delay. However, the results also showed that the VA-GMPR protocol exhibited higher energy consumption compared to EMGGR.