The finite horizon H-infinity control of time-invariant linear systems with a finite number of point and distributed time delays is considered. The controller is obtained by solving coupled Riccati-type partial differential equations. The solutions to these equations and the resulting controllers are approximated by series expansions in powers of the largest delay. Unlike the infinite horizon case, these approximations possess both regular and boundary layer terms. The performance of the closed-loop system under the memoryless zero-approximation controller is analyzed.