We report a candidate centi-parsec supermassive black hole binary (SMBHB) in the radio-quiet quasar SDSS J0159+0105 at z= 0.217. With a modified Lomb-Scargle code (GLSdeDRW) and auto-correlation analysis, we detect two significant (at P> 99%) periodic signals at ~741 day and ~1500 day from the 8.1 yr Catalina V-band light curve of this quasar. The period ratio, which is close to 1:2, is typical of a black hole binary system with a mass ratio of 0.05 < q< 0.8 according to recent numerical simulations. SDSS J0159+0105 has two SDSS spectroscopic observations separated by ~10 yr. There is a significant change in the broad Hbeta profile between the two epochs, which can be explained by a single broad-line region (BLR) around the binary system illuminated by the aforementioned mini-disks, or a stream of gas flowing from the circumbinary disk to one of the SMBHs. From the single BLR assumption and the orbital period t sub(orb)~ 1500 day, we estimate the total virial masses of M sub(SMBHB)~ 1.3 x 10 super(8)M sub(middot in circle), the average distances of BLR of ~0.04 pc (~50 lt-day, with + or -0.3 dex uncertainty), and an SMBHB separation of d= (0.01 pc)M super(1/3) sub(8.tot )(T sub(rest)/3.3 yr) super(2/3)~ 0.0.13 pc (15 lt-day). Based on analytical work, the postulated circumbinary disk has an inner radius of 2d= 0.026 pc (30 lt-day). SDSS J0159+0105 also displays unusual spectral energy distribution. The unique properties of SDSS J0159+0105 are consistent with it being a centi-parsec SMBHB.