A robust fractional-order linear super-twisting sliding mode observer (LSTSMO) for an induction motor speed sensorless system is proposed in this study to solve the problem of balance between sliding mode chattering and estimation accuracy. First, the stability of the linear super-twisting algorithm is proven with the Lyapunov function, and the convergence and gain coefficient range of the algorithm are analyzed. Next, the fractional integral sliding mode surface based on the stator current error term is established, and the linear super-twisting algorithm is introduced to design the fractional LSTSMO. In addition, a flux correction link is added to enhance the robust performance of the observer. The results of the simulations and experiments verify that the observer has high flux linkage estimation accuracy, which can enhance transient performance rapidity and chattering suppression ability simultaneously, thereby improving robustness against parameter drifts. Moreover, the designed observer improves the dynamic and steady state performance of the motor in the full-speed range.