We theoretically investigate quantum conductance across a point contact between two strongly-interacting ultracold Fermi gases. We evaluate the tunneling current, taking into account pairing fluctuations in the Fermi gases within the framework of a combined strong-coupling T-matrix approximation with the Schwinger-Keldysh non-equilibrium formalism. We show that quasi-particle conductance is gradually suppressed, as one passes through the BCS–BEC crossover region from the weak-coupling side. On the other hand, with increasing the strength of a pairing interaction, the fluctuation-pair conductance is found to remarkably increase in the crossover region, which is followed by the suppression in the strong-coupling regime.