Based on the generalized Huygens-Fresnel diffraction integral and the unified theory of coherence and polarization, properties of stochastic electromagnetic beams focused by a modulated lens are analyzed, the analytical expressions for the cross-spectral density matrix of a class of electromagnetic Gaussian Schell-model (EGSM) beams focused by an amplitude modulated lens are derived, and intensity distribution of EGSM beams focused by an amplitude modulated lens through numerical calculations is also analyzed. It shows that focused intensity distribution of EGSM beams is influenced by radius, location, transmittance of amplitude modulation, spatial position and the coherence length. When the radius of amplitude modulation takes a certain value, it appeares that focusing spot is extremely compressed and focusing central spot has a large energy at this time. Different shapes of intensity distribution can be gotten by changing the parameters of radius, location, transmittance of amplitude modulations and spatial position, and the coherence length.