A new predictive model reference adaptive system (MRAS) speed estimator was proposed to address the problem of the traditional proportional-integral (PI) adaptive rate in the induction machine (IM) drive system used for shield tunneling without a speed sensor. The traditional PI adaptive rate in the MRAS system relies on manual experience adjustment and cannot adapt to model changes. The proposed estimator was based on the principles of finite control set model predictive control. A search-based optimization algorithm was adopted during the rotor speed calculation, which ensures minimum speed adjustment error signals in each sampling period and avoids the use of a proportional integral controller. Experimental results show that the proposed speed estimator has excellent dynamic and static performance over a wide speed range.