We discuss a finite horizon H-infinity control problem for time-varying systems with input delays. Clarifying a relationship between two H-infinity control problems in input delay case and in measurement delay case, we derive a solution in input delay case based on the known result for the H-infinity control problem in measurement delay case, and show that the solution has the same predictor-observer structure as the solution in measurement delay case has. Using this structural information on the solution, we also present an elementary proof of the solution to the finite horizon H-infinity control problem for systems with input delays, which is based only on completion of squares. (C) 2004 Elsevier Ltd. All rights reserved.