We consider single production of the heavy top quark T predicted by the three-site Higgsless model in future high energy collider experiments,such as the high energy linear e+e- collider (ILC),the linear-ring type ep collider (THERA),and the CERN Large Hadron Collider (LHC).Our numerical results show that the possible signals of the heavy top quark T might be detected via the subprocess qb→ qT at the LHC.