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The fault estimation observer is designed for linear parameter varying multi-agent systems in finite frequency domain. First, the dynamic equation of each node is established according to the absolute measurable output and relative measurable output of each agent. The dynamic equation of multi-agent system is obtained by combining the undirected communication topology and Laplace matrix. The multi-agent system model was decoupled through appropriate transformation. Then, the fault estimation observer is designed based on the decoupled system dynamics equation, the gain matrix of the observer and the better robust performance index are obtained by the LMI optimization technique. Finally, the simulation of longitudinal flight motion of MAV are given to demonstrate the effectiveness of the designed fault estimation observer,when the system parameters change in a certain range, the fault estimation observer can still accurately estimate the faults occurring in the system.