This paper studies output-feedback time-varying formation (TVF) protocol design problems for general linear swarm systems with directed interaction topology. By adding extra observers, an adaptive output-feedback TVF protocol is constructed for general linear swarm systems with directed interaction topology to achieve a given TVF. Then, a fully distributed algorithm is proposed based on only local output information of each agent and its neighbors. Moreover, a sufficient condition for achieving the desired TVF under the designed adaptive output-feedback TVF protocol is derived based on the Lyapunov theory. Finally, a simulation example is presented to illustrate the theoretical results.