This paper studies the fault tolerant formation keeping problem of multi-agent systems with consideration of shortest connection topology. This is motivated by the requirement of low communication cost which largely depends on the communication length. Given a formation shape, a connection topology design method and its reconfiguration strategy are proposed in the sense that the whole connection path is shortest despite of communication faults. A control framework that combines the individual formation controller of each agent and connection topology is further presented. The stability of the whole system process is analyzed by switched system theories. Simulation results of unmanned aerial vehicles (UAVs) show the effectiveness of the proposed strategy.