In this paper, we present Greedy Routing for Maximum Lifetime (GRMax) [1],[2] which can use the limited energy available to nodes in a Wireless Sensor Network (WSN) in order to delay the dropping of packets, thus extend the network lifetime. We define network lifetime as the time period until a source node starts to drop packets because it has no more paths to the destination [3]. We introduce the new concept of Network Connectivity Aiming (NCA) node. The primary goal of NCA nodes is to maintain network connectivity and avoid network partition. To evaluate GRMax, we compare its performance with Geographic and Energy Aware Routing (GEAR) [4], which is an energy efficient geographic routing protocol and Greedy Perimeter Stateless Routing (GPSR) [5], which is a milestone among geographic routing protocol. We evaluate and compare the performance of GPSR, GEAR, and GRMax using OPNET Modeler version 15. The results show that GRMax performs better than GEAR and GPSR with respect to the number of successfully delivered packets and the time period before the nodes begin to drop packets. Moreover, with GRMax, there are fewer dead nodes in the system and less energy is required to deliver packets to destination node (sink).