The structural formation of polymer-nanoparticle composites (PNC), which are also called polymer spherical brushes, is investigated by Monte Carlo simulations. Based on an osmotic model, the solid-liquid transition of PNC systems due to the steric effect between PNCs is studied by employing the Lindemann criterion and the Hansen-Verlet criterion. The phase diagram of PNC systems is also clarified by the free-energy analysis of the system. These results indicate the existence of PNC crystals with sufficiently high density and the large number of polymer chains per each particle.