This study focuses on the problem of almost output regulation bumpless transfer control for switched linear systems. The authors aim at solving the almost output regulation problem with the bumpless transfer performance achieved via a multiple Lyapunov functions scheme. First, a concept of the bumpless transfer performance for a switched linear system is introduced. Then, a sufficient condition on the almost output regulation bumpless transfer performance of the system is obtained by dual design of a controller and a switching law. The sufficient condition allows that each subsystem does not satisfy the almost output regulation bumpless transfer property. Furthermore, a solution to the almost output regulation bumpless transfer control problem for the system is also offered in terms of linear matrix equalities and linear matrix inequalities. Finally, an example of controlling a turbofan model is given, showing that the proposed control strategy is effective.