Abstract: The problem of how to place the observers in passive testing while assuring they can monitor all the behavior of a network and the number of them is the smallest is an interesting and useful problem. First, this problem is proved to be an NP-complete problem. Then a special case in which the topology of network is a tree is discussed and a linear time algorithm for it is presented. Based on the thought of tree topology an improved approximate algorithm is proposed and the approximate proportion of the improved algorithm is 2-O(1). Finally, a simulating experiment is conducted to illustrate the effectiveness of the improved algorithm and future extensions are discussed.