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The reliability goal of wireless sensor network requires the network to be biconnected, so that the failure of one single node will not disturb the connectivity of the whole network. Wireless sensor network with uniform communication power and transmission radius is modeled as planar undirected graph. A search algorithm running in O(n3) polynomial time is proposed to find all the biconnected components in the wireless sensor network. Then all the articulation points in the network are found out. A greedy algorithm with worst case O(n2log(n/3)) polynomial time bound is proposed to place nodes as few as possible to achieve network biconnectivity. The new paths formed by the supplemented nodes help to decrease the number of relay hops between some sensor nodes and the sink node.