In this correspondence, the H-infinity control problem is studied for finite-dimensional linear time-varying (FDLTV) systems. State-space formulas are derived for all FDLTV controllers solving the problem, These controllers are parameterized by the interconnection of the "central controller" with an exponentially stable, free system having H-infinity norm strictly less than gamma, Our approach is drawn from some changes of variables, a time-varying version of a strict bounded real lemma, and Youla parameterization; thus, the proofs given are simple and clear.