The decentralized finite-time robust connective stabilization problem for a class of large-scale systems with expanding construction is studied. These large-scale systems with the expanding construction are the systems constituted by adding new subsystems on the original ones. The problem is to design the robust decentralized control law of the newly added subsystem on the basis of not changing the decentralized control laws of original construction, so that the expanded system can keep finite-time connective stability. The sufficient conditions of the decentralized finite-time connective stabilization for this kind of systems are deduced by using LMI method, which is based on state feedback and output feedback. And the design method of corresponding controller for expanding subsystem is given. Simulation results show the feasibility and effectiveness of the proposed method.