Abstract: The solitary Rossby waves with a critical layer in the nonuniformed zonal flows in the barotropic atmosphere are studied.After the KdV or the modified KdV equation which were satisfied by the streamfunctions had been gotten,the chebyshev polynomials and the pseudo-spectral method were applied in solving the eigenvalue problems.The computation of ideal wind field showed that whether there was a critical layer or not,the Subtropical high solitary Rossby waves which had the same evolution patterns as the actual subtropical high's can be obtained.And the blocking high solitary Rossby waves which also resemble actual blocking high's could be gotten too.Through a second method by calculating continuous and discrete spectrum on or near the critical layer,results similar to those chebyshev pseudospectral method are obtained.which conform our theory.