In this paper we study a free boundary problem modeling the growth of tumors with three cell populations: proliferating cells, quiescent cells and dead cells. The densities of these cells satisfy a system of nonlinear first order hyperbolic equations in the tumor, with tumor surface as a free boundary. The nutrient concentration satisfies a diffusion equation, and the free boundary satisfies an integro-differential equation. We consider the radially symmetric case of this free boundary problem, and prove that it has a unique global solution for all the three cases , and , where is the removal rate of dead cells. We also prove that in the cases and there exist positive numbers and such that for all , while in the case .