As a powerful tool for studying molecular dynamics in bioscience, single-molecule fluorescence detection provides dynamical information buried in ensemble experiments. Fluorescence in the near-infrared (NIR) is particularly useful because it offers higher signal-to-noise ratio and increased penetration depth in tissue compared with visible fluorescence. The low quantum yield of most NIR fluorophores, however, makes the detection of single-molecule fluorescence difficult. Here, we use asymmetric plasmonic nano-antenna to enhance the fluorescence intensity of AIEE1000, a typical NIR dye, by a factor up to 405. The asymmetric nano-antenna achieve such an enhancement mainly by increasing the quantum yield (to ~80%) rather than the local field, which degrades the molecules' photostability. Our coupled-mode-theory analysis reveals that the enhancements stem from resonance-matching between antenna and molecule and, more importantly, from optimizing the coupling between the near- and far-field modes with designer asymmetric structures. Our work provides a universal scheme for engineering single-molecule fluorescence in the near-infrared regime.