This work proposes an efficient disjoint multipath geographic routing algorithm for dense wireless sensor networks (WSN), called Multipath Grid-based Enabled Geographic Routing (MGEGR). The proposed algorithm relies on the construction of a 2-D logical grid in the geographical region of deployment. The objective of the proposed scheme is to determine optimal or near-optimal (within a defined constant) multiple disjoint paths (multipath) from a source node to the sink, in order to enhance the reliability of the network. The determined multiple disjoint paths would be used by the source node in a round-robin way to balance the traffic across the disjoint paths, and to avoid discovered paths with cell holes. The proposed scheme limits the use of broadcasting to the process of gateway election within each cell, and the process of maintaining the table of neighbors of each gateway. Our simulation results show the effectiveness and scalability of our routing scheme with increased network size compared to on-demand routing protocols.