It is well known that Serrin's universal stability criterion, by means of the energy method, gives an upper bound for the Reynolds number in order for a generic perturbation to exponentially decay in time. The original framework of the criterion is referred to the Navier-Stokes equations for a three-dimensional fluid in a periodic or bounded domain. In this paper the problem of the asymptotic non-linear stability of a quasi-geostrophic flow in a zonal channel is investigated. Two kinds of dissipation mechanisms are considered: the lateral diffusion of vorticity and the Ekman bottom dissipation. By using a procedure similar to Serrin's, a non-linear asymptotic stability criterion is obtained. The stability is governed by the maximum of the shear of the basic zonal current and the intensity of the dissipation parameters.