A ferroelectric field-effect transistor (FEFET) with a cylindrical ferroelectric (FE) nanopillar embedded in the gate oxide stack is proposed and investigated. The device utilizes the multiple polar topologi-cal states, which can be stabilized in a nanoscale regime. To correctly simulate the proposed FEFET, a full three-dimensional phase-field-based quantum transport model is developed where nonequilibrium Green's function, Poisson, and time-dependent Ginzburg-Landau equations are self-consistently solved. Using the in-house tool, we theoretically demonstrate that the nanopillar FEFET exhibits multibit oper-ation of six-level states with a reasonable memory window (MW) and sufficiently large difference in the current between the states. We also investigate the short-channel effect on the proposed FEFET and assess its scalability. MW linearly increases as the gate length decreases, because the polarization bound charges of the FE nanopillar induce the quasi-bound-states on the channel region and thus degrade the gate controllability.