Connectivity is one of the most important parameters in network monitoring. The connectivity model of Opportunistic Sensor Networks (OSN) can hardly be established by traditional graph models due to the fact that its connectivity is timing correlative and evolutionary, which makes it extremely difficult to monitor an OSN. In order to solve the monitoring problem, this paper builds an evolving graph model based on the theory of evolving graph as a description of an OSN. It defines a series of parameters to measure the connectivity of the OSN and establishes an monitoring model. Meanwhile, this paper gives the key algorithms in building the model, the Evolving-Graph-Modeling (EGM) algorithm and the Connected-Journey (CJ) algorithm. The rationality of the monitoring model has been proven by a prototype system and the simulation results. Extensive simulation results show that the proposed connectivity monitoring model can indicate real circumstances of OSN’ connectivity, and it is applicable to monitoring an opportunistic sensor network.