We studied the focusing properties of an anisotropic metamaterial slab lens by means of the angular spectrum representation of the vectorial electromagnetic field. The analytical expressions for vectorial fields in all the propagation regions are obtained，and the quantitative relationship between the focusing characteristics of the vectorial electromagnetic field and the anisotropic parameters of the anisotropic metamaterial slab lens is disclosed. The polarization state of the focusing beam is found to be changed due to the effect of anisotropy. As an application of the vectorial theory，we have analyzed the focusing property of an anisotropic metamaterial slab for which the permeability along longitudinal axis is -1. It is demonstrated that this slab lens can redirect a beam initially polarized along a transverse axis to a partial focus and give a clear polarization rotation of the beam.