This paper is concerned with the observer-based stabilization problem for linear systems with large delay periods (LDPs). The attention is focused on designing the full-order observers to guarantee the stability of the linear systems with LDPs. We use a switched system, which may include one subsystem that can not be stabilized, to describe such a model. First, the sufficient stability condition is presented for the system with small delay periods (SDPs). Then, the controller and the observer gains are designed based on the feasible solutions of LMIs. In the end, sufficient conditions guaranteeing the stability of the considered system with LDPs are presented.