Since the “free-riding” behavior objectively exists in a P2P network, how to precisely determine the “free-riders” in the network is now a key problem. Passive testing method has been the best way of finding the potential faults on the real network at present. The observer placement problem is one of the critical problems that have been played much attention on. The problem has been also proved to be a NP-complete problem. In this paper, a new DNA computing algorithm for the observer placement problem is produced. On the basis of the sticker-based model's solution space and the Adleman-Lipton model's biological operations, the algorithm consists of a pre-treatment algorithm, a vertex composer, a solution space generator, a parallel searcher and an observer placement searcher. Furthermore, we introduced greedy strategy into our new algorithm for reducing the solution space. In an experimental simulation, the algorithm is proved to have better storage utilization and fault tolerant ability.