This paper investigates the finite-time stabilization via the event triggered scheme of a maglev system with output constraint. Combining the finite-time trigger strategy with a time-varying threshold and a tangential barrier function, a new event-triggered controller is presented, which not only ensures that the suspension air gap of the maglev system is confined to a specified range but also guarantees that states converge to the origin within a finite time. The innovation lies in the fact that the design and the theory analysis for the constrained and unconstrained output are unified. Finally, the practical simulation is provided to demonstrate the effectiveness of the proposed method.