Model predictive control(MPC)is widely used in fast sampling systems owing to its fast reg-ulating ability.However,the sampling delay is a key issue and tends to be a fractional multiple of the sampling period.If the fractional-order delay is not accurately offset,the controller output will exhibit er-rors,thus resulting in oscillations in controlled system.Moreover,the MPC delay compensation algorithm is limited to the computation time.To address the problems of fractional delay and computational burden in fast sampling systems,we propose a new method to compensate for the fractional-order sampling delay.First,we use a finite-impulse-response fractional delay filter based on a Lagrange interpolation polynomial to approximate the fractional portion.Moreover,we prove that high accuracy and simplicity can be ensured when the polynomial order is one.Then,we estimate the current state variable using the delayed sampling signal and control signals of past moments.Further,we obtain the current control signal according to the estimated state variable.By considering the simultaneous existence of computational and sampling delays,a full compensation strategy is proposed.Computational simulation results validate the proposed MPC algorithm with fractional-order delay compensation and demonstrate its advantages.