A fast terminal sliding mode control method based on the finite time extended state observer(ESO) is proposed for the two mass servo systems with unknown load position information. To estimate the unknown disturbances, a finite-time extended state observer is designed and incorporated into the control design to compensate the unknown disturbance of two-mass systems. Then, combined with a new type of sliding mode reaching law, a non-singular fast terminal sliding mode controller is proposed, which can eliminate singularity existing in the conventional sliding mode control. Therefore, a finite time sliding mode controller is designed based on the ESO, which improves the reaching speed of sliding mode variables and ensures that the system state converges to the origin in finite time. The finite time stability of the closed-loop control system is analysed via the Lyapunov stability theory. Comparative simulations and experiments are carried out based on a two-mass driving system to validate the effectiveness of the proposed approach.