Extensive molecular dynamics simulations are performed for a hard-sphere fluid at 6% polydispersity. The simulation results are then analyzed based on the mean-field theory proposed recently by Tokuyama (Physica A 364, 23-62 (2006)). The phase diagram and the dynamic behavior are investigated fully in each phase. It is then found that as the volume fraction is increased, a supercooled liquid phase appears at the supercooled point β (≃ 0.5524) and a transition from supercooled liquid to crystal then occurs at the melting volume fraction m(1)(≃0.5625). As is further increased, a transition from crystal to supercooled liquid (re-entrant melting) is also observed at the second melting volume fraction m(2)(≃0.5770) within a waiting time tw = 7 × 104t0, where t0 is a time for a particle to move over a distance of a particle radius with an average velocity. The glass transition is thus predicted to occur at the glass transition volume fraction g (≃ 0.6005). The various aspects obtained in our study is quite similar to those in the experiment for the suspension of hard spheres, including the logarithmic growth of the mean-square displacement in fast-β stage, the non-singular behavior of the long-time self-diffusion coefficient, and the non divergence of any characteristic times, such as the α- and β-relaxation times.