We study the long-term variability in the optical monitoring database of Ark 120, a nearby radio-quiet active galactic nucleus (AGN) at a distance of 143 Mpc (z = 0.03271). We compiled the historical archival photometric and spectroscopic data since 1974 and conducted a new two-year monitoring campaign in 2015-2017, resulting in a total temporal baseline over four decades. The long-term variations in the optical continuum exhibit a wave-like pattern and the H beta integrated flux series varies with a similar behavior. The broad H beta profiles have asymmetric double peaks, which change strongly with time and tend to merge into a single peak during some epochs. The period in the optical continuum determined from various period-search methods is about 20 yr, and the estimated false alarm probability with null hypothesis simulations is about 1 x 10 (-3). The overall variations of the broad H beta profiles also follow the same period. However, the present database only covers two cycles of the suggested period, which strongly encourages continued monitoring to track more cycles and confirm the periodicity. Nevertheless, in light of the possible periodicity and the complicated H beta profile, Ark 120 is one candidate of the nearest radio-quiet AGNs with possible periodic variability, and it is thereby a potential candidate host for a sub-parsec supermassive black hole binary.