The surface-initiated polymerization with different initiator densities and different polymerization rates is investigated using molecular dynamics simulation method. We find that the initiator density, together with the polymerization rate, greatly determines the polymer brush structure, the initiation efficiency, and the graft density, especially when the initiator density is high. The excluded volume effect also plays a crucial role in the system when the chains are densely grafted. By tuning the initiator density and modifying the polymerization rate, we can obtain the polymer brushes with different degrees of polydispersity. This Study partially emphasizes the importance of considering the effects of polymerization rate in further investigations.