Based on vectorial Debye theory, the focusing properties of stochastic electromagnetic vortex beams by a high numerical aperture objective are investigated. The influence of numerical aperture of the objective, the degree of polarization, the topological charges, and the transverse coherent length of the incident vortex beam on the intensity and spectral degree of coherence in the focal region are investigated. Studies in intensity distribution reveal that elliptical light spots and the flat top beam, which have many applications, can be obtained by selecting certain parameters. The degree of coherence at a point between two orthogonal electric field components, the degree of coherence at a pair of points between two identical electric field components, and the degree of coherence at a pair of points between two orthogonal electric field components of stochastic electromagnetic vortex beams in the focal plane are investigated respectively. It is shown that the topological charges and transverse coherent length of incident vortex beams have very obvious effects on the coherence of focused beams.