The paper proposes a type of unbiased finite impulse response(UFIR) filtering algorithm for the discrete time-varying linear state space model with state delay. By constructing the augmented system vector comprising delay, the original system model is transformed into a non-delay counterpart. Then, the extended state-space model is developed, from which the traditional UFIR filtering algorithm is generalized to the state-delayed system with control input, which provides convenience for practice. Further more, the corresponding iterative form is developed, and the speediness feature like Kalman is preserved. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method.