: Leader election algorithms solve the instability problem in the network which is caused by leader failure .In this paper, we propose a new leader election algorithm in two dimensional torus networks. The algorithm aims to elect one node to be a new leader. The new leader is identified by some characteristics not in the other nodes in the network. When the process is terminated, the network is returned to a stable state with one node as leader where other nodes are aware of this leader. The new algorithm solves this problem despite the existence of one link failure. In a network of N nodes connected by two dimensional torus network, the new algorithm uses O(N) messages to elect a new leader in O( N ) time steps. These results are valid for both cases: simple case (when the leader failure is detected by one node) and in the worst case (when the failure is discovered by up to N-1 nodes).