For elevators, appropriate speed control is pivotal for ensuring the safety and comfort of passengers and optimizing energy efficiency, system stability, and service life. Therefore, the design and implementation of effective speed control strategies are crucial for the operation and management of modern elevator systems. In response to this issue, this paper establishes a dynamic model of an elevator through mechanism analysis. Then, a novel fractional-order sliding mode control strategy with the assistance of a fixed-time adaptive sliding mode observer is proposed. The designed observer can effectively monitor and counteract external perturbations, thereby enhancing the stability and precision of the control system. The fractional-order sliding mode controller can realize a fixed-time convergence property, which is rigorously proven in the sense of Lyapunov. Finally, the effectiveness and superiority of the control scheme are validated by simulations compared with benchmark controllers.