In this letter, motivated by double-peaked broad Balmer emission lines probably related to tidal disruption events (TDEs), a potential TDE candidate is reported in SDSS J160536+134838 (=SDSS J1605) at z ∼ 0.44 having quasar-like spectrum but with double-peaked broad Hβ. The long-term CSS light curve can be naturally described by a main-sequence star of $2.82_{-0.19}^{+0.20}{\rm M_\odot }$ disrupted by the central black hole (BH) of $144_{-21}^{+26} \times 10^6{\rm M_\odot }$ in SDSS J1605. Meanwhile, the ASAS-SN light curves afterwards show none apparent trend variability, indicating the bright CSS flare in SDSS J1605 unique and different enough from variability of normal AGN. Furthermore, there is a consistency between the TDE model determined sizes of debris with the sizes of emission regions for the double-peaked broad Hβ described by the accretion disk model, supporting the disk-like BLRs probably related to a central TDE in SDSS J1605. And the virial BH mass ∼7 times higher than the TDE model determined value can be naturally explained by R-L relation determined BLRs sizes very larger than the actual distance of emission regions related to TDEs debris in SDSS J1605. Although no clear conclusion on double-peaked broad lines absolutely related to TDEs, the results here provide clues to detect potential TDEs in AGN with double-peaked broad lines.