The permanent magnet linear synchronous motor (PMLSM) is a promising motor to drive cordless elevator, computer numerical control machines due to its high force density and zero transmission. In the presence of rapidly varying loads, however, the conventional control methods of PMLSM cannot guarantee the precise-velocity and high-dynamic operation. In this work, a large signal stabilization scheme, which comprises finite-time observer (FTO) and a finite-time controller (FTC), is proposed. Firstly, a finite-time observer is introduced to accurately observe the varying loads in finite time. Secondly, the FTC exactly offsets the estimated values and stabilizes all system states at their designated points in finite time. Finally, numerical simulation results show that the proposed controller provides a stronger adaptability and better performance in precision and speed to rapidly varying loads than the traditional PI controller.