Abstract: The global stability and convergence of the explicit GPC (generalized predictive control) based on CARMA model are proved by employing the state-equation, in which the extended least-square method is taken as the identification method. It is shown in theory that the GPC algorithm based on CARMA is better than some currently used self-tuning algorithms such as the generalized minimum-variance method and pole-placement method, and so on, because it has good stability and convergence even underweaker conditions.