The interaction between two spiral waves in two-layer excitable medium coupled indirectly through a passive medium and with time-delayed coupling is investigated by using the Bär model. The numerical results show that time-delayed coupling can either facilitate the synchronization of two spiral waves or lead to the transition from spiral wave to collective oscillation, different target waves, spatiotemporal chaos or rest state. Period-2 and period-3 spiral waves and the meander or drift of spiral wave are observed in the coupled excitable medium. The physical mechanism underlying these phenomena is discussed.