Surface plasmons are collective electron excitations in metallic systems, and the associated electromagnetic wave usually has the transverse-magnetic polarization. On the other hand, spin waves are spin excitations perpendicular to the equilibrium magnetization and are usually circularly polarized in a ferromagnet. The direct coupling of these two modes is challenging due to the difficulty of matching electromagnetic boundary conditions at the interface of magnetic and nonmagnetic materials. Here, we overcome this challenge by utilizing the linearly polarized spin waves in antiferromagnets (AFM) and show that a strong coupling between AFM magnons and surface plasmons can be realized in a hybrid two-dimensional (2D) material/AFM structure, featuring a clear anticrossing spectrum at resonance. The coupling strength, characterized by the gap of anticrossing at resonance, can be tuned by electric gating on 2D materials and probed by measuring the two reflection minima in the reflection spectrum. Further, as a potential application, we show that plasmonic modes can mediate the coupling of two well-separated AFMs over several micrometers, featuring symmetric and antisymmetric hybrid modes. Our results may open a platform to study antiferromagnetic spintronics and its interplay with plasmonic photonics.