This paper proposes an adaptive motion control system for a linear motor single-axis robot, which is mainly composed of a linear induction motor (LIM). On the basis of indirect field-oriented control mechanism, the dynamics of linear motor robot is investigated for considering the time-varying uncertainties that exist in the LIM drive. Next, a backstepping controller is designed for the objective of tracking periodic reference trajectories. To relax the prior knowing of the system uncertainties which are lumped by a conservative constant, a self-organizing fuzzy controller is hybridized into the backstepping controller so that the lumped uncertainties can be confronted in practical applications. The experimental results including good tracking performance against uncertainties can verify the effectiveness of the proposed control scheme.