This paper presents a method for compensation of unknown bounded smooth disturbances for linear time invariant (LTI) plants with known parameters in the presence of constant and known input delay. The proposed control law is a sum of the classical predictor suggested by Manitius and Olbrot for finite spectrum assignment and a disturbance compensator. The disturbance compensator is a novel control law based on the auxiliary loop for disturbance extraction and on the disturbance prediction. A numerical implementation of the integral terms in the predictor-based control law is studied and sufficient conditions in terms of linear matrix inequalities are provided for an estimate on the maximum delay that preserves the stability. Numerical examples illustrate the efficiency of the method.