The design of routing protocols is crucial for mobile ad-hoc networks due to their fast-changing characteristics. Most of the ad-hoc routing algorithms are designed based on extensive flooding of control packets, which result in excessive overheads within the networks. The greedy routing algorithms employ localized information from the mobile nodes (e.g. relative distance or direction), which induce comparably less control packets in the networks. However, several problems (e.g voids, loops, or dead-ends) are encountered in most of the greedy algorithms due to the localized characteristics. In this paper, a Largest Forwarding Region (LFR) routing protocol is developed. The mobile node with the largest Extended Forwarding Region (EFR) is selected as the next hopping node for packet forwarding. The associated Backward Constraint (BC) and Dead-End Recovery (DER) mechanisms further alleviate the problems resulting from voids in the networks. The performance comparison between the proposed LFR algorithm and other existing greedy routing schemes is conducted via simulations. It is observed that the LFR scheme effectively increases the packet arrival rate without creating excessive control overheads.