In this letter, a new estimation filtering is proposed when a delay between signal generation and signal estimation exists. The estimation filter is developed under a maximum likelihood criterion using only the finite observations on the delay interval. The proposed estimation filter is represented in both matrix form and iterative form. It is shown that the filtered estimate has good inherent properties such as time-invariance, unbiasedness and deadbeat. Via numerical simulations, the performance of the proposed estimation filtering is evaluated by the comparison with that of the existing fixed-lag smoothing, which shows that the proposed approach could be appropriate for fast estimation of signals that vary relatively quickly. Moreover, the on-line computational complexity of the proposed estimation filter is shown to be maintained at a lower level than the existing one.