Based on the extended Huygens-Fresnel principle, the propagation formulas for focusing of partially coherent electromagnetic vortex beams by an aperture lens have been derived. Based on these formulas, the intensity distribution and the degree of coherence near the geometrical focus are investigated. It is found that the topological charges, normalized coherence lengths and the truncated parameter play an important role in controlling the size of the partially coherence vortex dark core and the distribution of coherence in the focal region. The size of the vortex dark core increases with increasing the topological charge and the normalized coherent length. Moreover, the intensity of the vortex bright ring moves to the aperture with decreasing the normalized coherent length and the perceptive parameter. The effective coherent length in the focal region decreases with increasing the normalized coherence lengths and topological charges. It is also found that the effective coherent length increases with increasing the propagating distance. Therefore, the desired vortex dark core near the geometrical focus can be achieved by choosing appropriate values of parameters.