This paper proposes an adaptive observer for an active leader and designed a distributed observer-based control law for the formation control of networked uncertain offshore vessels under the switching topologies. The design of the observer, only depending on the output of the leader system, is featured with the ability of accurately estimating the output of the leader system with an unknown input over the time-varying communication network, satisfying the periodic switching condition. Then based on the output-based observer, the formation problem of multiple offshore vessels is converted into the stabilization problem of a multi-input multi-output augmented system by further combining the internal model technique and performing a coordinate and input transformation. The original problem is finally solved through constructing a stabilizer for the time-varying uncertain augmented system, and the efficiency of our design is validated by the formation control of a group of offshore vessels.