In a simplified model including an SU (2) singlet T quark with charge 2/3, we investigate the single vector-like T production at the high energy eγ collision. We study the observability of the vector-like T focusing on the T→Wb decay channel with W→lν¯ at s=2.0 TeV. In this analysis, only two free parameters are involved, namely the T quark coupling strength for single production g∗ and the mass mT . We scan the parameter space and find that the correlation region of g∗∈[0.24,0.5] and mT∈[800,1360] GeV can be excluded with integrated luminosity L=100fb-1 and the correlation region of g∗∈[0.13,0.5] and mT∈[800,1620] GeV can be excluded with integrated luminosity L=1000fb-1 at 2σ level.