Cooperative monitoring targets of mobile robots is of great importance in military, civil, and medical applications. In order to achieve multi-robot coordinated monitoring, this paper proposes a new distributed path planning algorithm. In this algorithm, a method of dynamic sequential decision making is used firstly to determine which robots should be moved to the neighbourhoods of the target path. A distributed cooperative path planning algorithm is then proposed in which the robots can only utilize their local information to make the joint monitoring areas of robots cover the target path. To reduce the chance of detection and ensure enough time to implement monitoring handover, our distributed algorithm can guarantee enough overlapped monitoring areas between adjacent robots. The effectiveness of the algorithm was verified by simulation experiments and a comparison experiment in typical scenarios.