Based on a simplified model including a singlet vector-like top quark T with charge |Q|=, we analyze the prospects of observing T via the single T production in the channel with Z decaying to neutrinos at the hadron-hadron colliders. This simplified model only includes two free parameters, the coupling constant and the T quark mass . To investigate the observability of the single T production, we perform a detailed background analysis and detector simulation for the collision energies 14 TeV, 27 TeV, and 100 TeV. We scan the parameter space and show the exclusion and discovery capabilities on the T quark with the highest integrated luminosity designed at these colliders. Moreover, the limits from the narrow-width approximation and electroweak precision observables are considered.