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We present a gauge invariant linear response theory for ultra-cold Fermi gases undergoing BCS-BEC crossover with pair fluctuation effect.Below Tc,the construction of a gauge invariant vertex is non-trivial,because the effects of Nambu-Goldstone modes(collective modes)intertwines with that of the pairing fluctuation.We focus on the G0G t-matrix approach to the pair fluctuations,although our formalism should also works equally well for the G0G0 t-matrix theory.