We report a large enhancement of thermally injected spin current in normal metal (NM)/antiferromagnet (AF)/yttrium iron garnet (YIG), where a thin AF insulating layer of NiO or CoO can enhance the spin current from YIG to a NM by up to a factor of 10. The spin current enhancement in NM/AF/YIG, with a pronounced maximum near the Néel temperature of the thin AF layer, has been found to scale linearly with the spin-mixing conductance at the NM/YIG interface for NM=3d, 4d, and 5d metals. Calculations of spin current enhancement and spin mixing conductance are qualitatively consistent with the experimental results.