Unlike traditional coherent laser beams, the beam quality evaluation of partially coherent beams involves not only its far-field radiation characteristic but also partial coherence of the light source itself. The generalized expression for the phase-space product Q of a beam generated from a partially coherent source is presented by using coherent-mode representation of partially coherent beams. Compared with the result for the fully coherent light source obtained in previous works, the derived expression for Q includes not only contributions directly from the linear combination of each individual elementary fully coherent modes but also interactions between different elementary modes.