A novel distributed adaptive output feedback control strategy is developed to solve the cooperative output regulation problem of heterogeneous general linear multi-agent systems(MASs) under switching topology. The proposed control strategy avoids using the minimal non-zero eigenvalue of Laplacian matrix when calculating gain matrix, and the communication topology is assumed to contain a directed spanning tree only frequently. It is shown that individual agents could track external signal asymptotically and achieve disturbance rejection. Ultimately, a simulation is presented to exemplify the effectualness of the main result.