We have assembled the historical light curves of the BL Lac Object 3FGL J0449.4-4350 at optical and gamma-ray bands, the time spanning about 10 years, analyzed the periodic variability of the light curves by using four different methods (Lomb-Scargle periodogram, REDFIT38, Jurkevich and DACF). We detected a marginally possible quasi-periodic oscillation (QPO) of ~450 days. Assuming it originates from the helical motion jet in a supermassive binary black hole (SMBBH) system undergoing major merger, we estimate the primary black hole mass M~7.7*10^{9} M_sun. To explore the origin of the gamma-ray, we investigated the optical-gamma-ray correlations using discrete correlation function (DCF) method, and found that the correlation between the two bands is very significant. This strong correlation tends to imply lepton self-synchro-Compton (LSSC) model to produce the gamma-ray.
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