Linear induction machines (LIMs) find widespread adoption in various applications, owing to their inherent advantages such as low noise, compact turning radius, and excellent climbing capability. LIMs are extensively utilized in linear metro applications. However, in practical operations, the output thrust shrinks with the increase in speed, which is attributed to end effects. This phenomenon leads to a reduction in efficiency. In addition, fluctuations in the normal force impact system stability, posing disturbances to the suspension system. To address these challenges, this paper suggests a finite-set model predictive thrust control (FS-MPTC) for a drive system employing a linear induction motor (LIM). The FS-MPTC optimizes the duty cycle for the active voltage vector and allocates the remaining period to one of the zero voltage vectors. The selected zero voltage vector reduces the switching transition between it and the active voltage vectors. The duty cycle is calculated for the six voltage vectors by incorporating the deadbeat concept and the derivative value for the electromagnetic thrust. In the prediction stage of the FS-MPTC, the computed duty cycle and the corresponding voltage vector are used simultaneously and repeated for the six voltage vectors. The cost function comprises two terms: the error between the reference thrust and predicted thrust value as the first term and the error between the rated primary flux linkage and its predicted value as the second term. The reference thrust is generated from the outer speed control loop. To validate the effectiveness of the proposed control approach, Japanese 12000 linear induction machine parameters are employed for verification. Comparative analysis of the performance between the suggested control method with the optimal duty cycle and the same process with a fixed duty cycle demonstrates superior performance when utilizing the optimal duty cycle. Finally, the proposed FS-MPTC with the optimal duty cycle offers a promising solution to enhance the operational efficiency of the LIM-based drive systems.