We study the decay t → cγ with flavor-changing neutral interactions in scalar sector of the type III Two Higgs Doublet Model (THDM-III) with mixing between neutral scalar fields as a result of considering the most general scalar potential. The branching ratio of the decay Br (t → cγ) is calculated as function of the mixing parameters and masses of the neutral scalar fields. We obtain a Br (t → cγ) of the order of 10−8 for the considered regions of the mixing parameters. Finally, one upper bound for the possible events is estimated to be n=18 by assuming an expected luminosity of the order of 300 fb−1.