As a natural consequence of cosmological hierarchical structure formation, sub-parsec supermassive black hole binaries (SMBHBs) should be common in galaxies but thus far have eluded spectroscopic identification. Based on four decades of optical spectroscopic monitoring, we report that the nucleus of NGC5548, a nearby Seyfert galaxy long suspected to have experienced a major merger about 1 billion yr ago, exhibits long-term variability with a period of ∼14 yr in the optical continuum and broad Hβ emission line. Remarkably, the double-peaked profile of Hβ shows systematic velocity changes with a similar period. These pieces of observations plausibly indicate that an SMBHB resides in the center of NGC5548. The complex, secular variations in the line profiles can be explained by orbital motion of a binary with equal mass and a semimajor axis of ∼22 light-days (corresponding to ∼18 milli-parsec). At a distance of 75Mpc, NGC5548 is one of the nearest sub-parsec SMBHB candidates that offers an ideal laboratory for gravitational wave detection.