A suspension of colloidal particles and polydisperse polymer coils is modeled using the hard-sphere potential for the colloid and the Asakura-Oosawa model for the colloid-polymer interaction [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The phase behavior of the mixtures is compared with that for a monodisperse polymer [H. N. W. Lekkerkerker et al., Europhys. Lett. 20, 559 (1992)]. Polydispersity is seen to increase the extent of the fluid-fluid coexistence found if the radius of gyration of the polymer is sufficiently large. The partitioning of polymer coils of different sizes between coexisting phases is studied.