This paper proposes a nonlinear speed controller in order to avoid the tracking speed problem of the finite-set model predictive current control (FS-MPCC) for linear induction machine (LIM). The speed of the LIM is regulated using the terminal sliding mode controller (TSMC) instead of the conventional PI controller aiming to achieve faster dynamic response with less steady-state error. The output of the TSMC serves as the q-axis primary current reference of the FS-MPCC. The mathematic model of the proposed TSMC based on FS-MPCC is implemented in the αβ frame instead of the dq frame to decrease the computation time and avoid the complex frame transformation. Finally, the control performance of the proposed strategy is verified by simulation and experiments which are based on the platform of two 3 kW arc induction machines (demonstration on the LIM performance in practice).