In a distributed system, a portion of nodes are more critical than others, and named them articulation points, all paths between certain nodes have to pass through these points. Most of previous works try to detect the articulation point problem in static networks such as wireless sensor networks, P2P networks. In dynamic networks, as group moving behavior, it is a challenge to detect articulation points because these nodes are moving with time. Group moving in this paper means that a group of mobile members move from one place to another place with different directions and speeds. We aim to propose a distributed LDFS algorithm to check the articulation points in dynamic networks, such as a moving group. The algorithm sets the number of hops for traversing and multiple initiators to reduce message overhead and improve the accuracy rate. In simulations, we design several schemes to compare message overhead, and correctness. Simulation results show that our scheme is better than GlobalDFS and CUD scheme. The scheme could be applied on different applications and is efficient helping us to save and alarm loss on group moving.