A new 4×4 complex curvature tensor Μ-1 is introduced to describe partially coherent anisotropic Gaussian-Schell model beams (GSM). The propagation law of Μ-1 is also derived which may be called partially coherent tensor ABCD law. The focusing properties of GSM beam focused by a thin lens using the derived tensor ABCD law of partially coherent are calculated and analyzed. The result shows that the focusing properties of partially coherent GSM beam are closely related to the coherence length and phase front curvature. For the case of partially coherent anisotropic GSM beam, its focusing properties are also related to the twist factor.