Due to the current constraint of linear induction machine (LIM) and voltage constraint of inverter, the output thrust of LIM is limited. So, in order to make LIM output thrust as large as possible within current and voltage limit, firstly, the maximum thrust per ampere (MTPA) is used to achieve maximum thrust with limited current in low speed. Secondly, with the speed of LIM increasing, the voltage limit of inverter has to be considered by the method of field-weakening. And similar to the concept of MTPA, the maximum thrust per volt (MTPV) is deduced for achieving maximum thrust within the voltage constraint of inverter. Finally, the deadbeat control method is applied to LIM for high tracking performance, and both simulation and experiments demonstrate the effectiveness of this proposed control strategy.