In an extension of the Standard Model with vector-like top partner, we investigate the vector-like top quark partner T via the channel at future linear collider. Due to the larger production rates than unpolarized beams, we calculate the production cross sections in polarized beams at and 3 TeV. We make a fast detector simulation for signal and background events and take a set of appropriate kinematic variables to enhance the signal significance. When the initial state radiation and beamstrahlung effects are in charge, we find that the correlated region () and () can be excluded at 2σ level with the integrated luminosity () at TeV. When the center-mass energy is upgraded to 3 TeV, the excluded region is expanded to () and () with the integrated luminosity (). Besides, we find the 5σ discovery correlated region is () and () with the integrated luminosity at TeV (3 TeV).