The dynamics of the feedback control model on a single population with piecewise constant arguments and interference are investigated in this paper. A difference model which can equi-valently describe the dynamical behavior of the original differential model is deduced. Based on the analysis of the eigenvalues and Schur-Cohn criterion, the sufficient conditions for local asymptotic stability of the positive equilibrium are achieved. Moreover, by choosing the intrinsic growth rate of the population as the bifurcation parameter and applying the bifurcation and center manifold theories, the existence conditions for the Neimark-Sacker bifurcation of this difference model is derived. Finally, some numerical examples substantiating our theoretical predictions are given and the numerical simulations also show that: 1) the dynamics of the single population of feedback control model are very complex when we consider piecewise constant arguments and interference; and 2) the positive equilibrium of the model switches from stable to unstable as the intrinsic growth rate of population increases beyond a critical value, at which the unique supercritical Neimark-Sacker bifurcation will occur.