Excitation and manipulation of surface plasmons (SPs) are essential in developing cutting-edge plasmonic devices for medical diagnostics, biochemical spectroscopy and communications. The most common approach involves designing an array of periodic slits or grating apertures that enables coupling of the incident light to the SP modes. In recent years, plasmonic resonances, including extraordinary optical transmission through periodic arrays, quasicrystals and random aperture arrays, have been investigated in the free space. However, most of the studies have been limited to the far field detection of the transmission resonance. Here, we perform near-field measurements of the SPs on quasicrystal metasurfaces. We discover that the reciprocal vector determines the propagation modes of the SPs in the quasicrystal lattice which can be well explained by the quasi-momentum conservation rule. Our findings demonstrate vast potential in developing plasmonic metasurfaces with unique device functionalities that are controlled by the propagation modes of the SPs in quasicrystals.