We present a fully vectorial description of the focusing of electromagnetic beams by a slab of indefinite media, in which waves can exhibit dispersion surfaces in the form of an ellipsoid, a double-sheeted hyperboloid, or a single-sheeted hyperboloid. Firstly, by means of the angular spectrum representation for electromagnetic beams, we analyze the transmission properties of a paraxial beam through a slab of indefinite media with the different dispersion relations, respectively. We found that a paraxial beam undergoes focusing in both x and y axes for the slab with an ellipsoid dispersion relation, and undergoes focusing or dispersion in different axes for the slab exhibiting a dispersion surface of a single-sheeted hyperboloid; while the beam cannot transmit in the slab with a double-sheeted hyperboloid dispersion relation. The inherent physics underlying these phenomena is that the effective refractive indices of indefinite media with different kinds of dispersion relations have different sign combinations. Secondly, the paraxial scheme is generalized to describe the propagation of slightly nonparaxial beams in the indefinite media slabs and the nonparaxial correction to the paraxial solution is derived. It is demonstrated that the contribution of nonparaxial correction to the longitudinal component is greater than the corresponding contribution to the transverse component. Importantly, we find that, due to the coupling effect of vectorial field components in indefinite media, the beam suffers a slight change of polarization state.