This paper is concerned with approximate controllability of a nonlinear hierarchical age-structured population model. Based upon the core assumption that the mortality and fertility of an individual of age $a$ depend more on the number of individuals with age older than $a$, the state system is described by an integro-partial differential equation with a globally feedback boundary condition, and the control policy stands for the migration process (inflow or emigration). For the strongly nonlinear population system, the distributed approximate controllability is established by combining frozen coefficients and the Ky Fan-Glicksberg fixed point theorem of set-valued maps with a controllability result of a linear system in the literature.