Summary: We propose a system of nonlinear differential equations for the study of growth of a single-species, age-structured population. A single-species population is divided into two groups: immatures and matures. We consider a nonlinear density-dependent death rate for the immatures. The death rate for the matures is taken to be logistic. We show the positivity and boundedness of solutions of the system. We consider the problem of the existence and uniqueness of equilibria for the system. Finally, we show that under appropriate conditions, the equilibrium at the origin is unstable while the equilibrium in the positive plane is locally asymptotically stable.