The finite time horizonH∞-control problems for nonlinear time-varying systems are considered where the initial state is unknown. They are solved by using both static state feedback and dynamic output feedback controllers. A class of nonlinearH∞-controllers is parameterized as nonlinear fractional transformation on contractive nonlinear parameters. The solvability for nonlinear finite time horizonH∞-control problem requires suitable solutions to some Hamilton-Jacobi inequalities (equations).