We report the finding of an unobscured type II Active Galactic Nuclei (AGN) candidate, SDSS J012032.19-005501.9 at a relatively high redshift of 0.601,which shows a number of unusual properties. It varies significantly on timescales of years as typical type I AGNs and marginally on timescales of weeks. The color-magnitude relation and the structure function are also consistent with that of type I AGNs, which imply that its variability likely originates from the black hole accretion system .However, no broad emission line is detected in the SDSS spectrum, and the upper limit of the equivalent width of the H$rm beta$ broad emission line is much less than that of type I AGNs. These properties suggest that SDSS J012032.19-005501.9 may be an unobscured quasar without broad emission lines intrinsically, namely an unobscured type II AGN or true type II AGN. Furthermore, its continuum luminosity is at least one order of magnitude fainter than the average value of thepast century expected from the [OIII] emission line. It indicates that SDSS J012032.19-005501.9 may be switching off. Additional possible scenarios to explain this intriguing source are also discussed. Future deep observations at multi-wavelengths are needed to reveal the nature of this peculiar and intriguing AGN.
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