Based on the Euler-Bernoulli beam theory, a dynamical model of piezoelectric coupling beam subjected to axial force and delayed-feedback was derived. The stability conditions of the system under piezoelectric coupling and delayed feedback was investigated through modal analysis and linear stability analysis. The Galerkin method and multi-scale method were used to study the bifurcation response of the time delay system. Numerical simulation was employed to study the effects of control gain on the dynamics of the system, i.e., stability and bifurcation of an equilibrium point, periodic solution, period-doubling, quasi-periodic motion and even chaos.