Joint acceleration feedback is widely used in the design of controllers and observers since joint accelerations reflect the joint dynamics of robots, especially in physical human-robot interaction. However, joint acceleration acquisition is a technical difficulty for robots. The dynamics-based methods can achieve joint acceleration estimation using only a nominal model. Still, the performance of these methods is limited by the fast time-varying disturbances in the system. This letter proposes a joint acceleration estimation method based on a high-order disturbance observer. This method can observe and compensate for fast time-varying lumped disturbances in the observer while maintaining joint acceleration estimation performance at low frequencies. The finite-time stability of the proposed estimation method is proved using the Lyapunov theory. Simulations and experiments with a lower limb rehabilitation robot are implemented to verify the performance of the proposed method.