In this paper, the problem of H. output feedback control for switched linear discrete-time systems with time delays is investigated. The time delay is assumed to be time-varying and bounded. By constructing a switched quadratic Lyapunov function for the underlying system, both static and dynamic H-infinity output feedback controllers are designed respectively such that the corresponding closed-loop system under arbitrary switching signals is asymptotically stable and a prescribed H-infinity noise-attenuation level bound is guaranteed. A cone complementary linearization algorithm is exploited to design the controllers. A numerical example is presented to show the effectiveness of the developed theoretical results.