In many traditional On Demand routing algorithms in Ad hoc wireless networks, a simple flooding mechanism is used to broadcast route request (RREQ) packets when there is a need to establish a route from a source node to a destination node. The broadcast of RREQ may lead to high channel contention, high packet collisions, and thus high delay to establish the routes, especially with high density networks. Ad hoc on Demand Distance Vector Routing Protocol (AODV) is one among the most effective Reactive Routing Protocols in MANETs which use simple flooding mechanism to broadcast the RREQ. It is also used in Wireless Sensor Networks (WSN) and in Vehicular Ad hoc Networks (VANET). This paper proposes a new modified AODV routing protocol EGBB-AODV where the RREQ mechanism is using a grid based broadcast (EGBB) which reduces considerably the number of rebroadcast of RREQ packets, and hence improves the performance of the routing protocol. We developed a simulation model based on NS2 simulator to measure the performance of EGBB-AODV and compare the results to the original AODV and a position-aware improved counter-based algorithm (PCB-AODV). The simulation experiments that EGBB-AODV outperforms AODV and PCB-AODV in terms of end-to-end delay, delivery ratio and power consumption, under different traffic load, and network density conditions.