Surface plasmon polaritons (SPPs) propagating at metal nanostructures play an important role in breaking the diffraction limit. Chemically synthesized single-crystalline metal nanoplates with atomically flat surfaces provide favorable features compared with traditional polycrystalline metal films. The excitation and propagation of leaky SPPs on micrometer sized (10-20 μm) and thin (30 nm) gold nanoplates are investigated utilizing leakage radiation microscopy. By varying polarization and excitation positions of incident light on apexes of nanoplates, wave-vector (including propagation constant and propagation direction) distributions of leaky SPPs in Fourier planes can be controlled, indicating tunable SPP propagation. These results hold promise for potential development of chemically synthesized single-crystalline metal nanoplates as plasmonic platforms in future applications.