Based on the Euler-Bernoulli beam theory and Reissner principle, the equations of the non-linear response of a composite laminated buckled beam with clamped ends and a lumped mass to an axial periodic excitation were obtained. By using the singlemode approximation and Galerkin's method, the differential equation was derived, and the bifurcation diagram of displacement varying with the excitation amplitude was obtained by using the fourth-order Runga-Kutta algorithm. Moreover, the effect of size and locations of the concentrated mass on the natural frequency and period-doubling bifurcation was discussed.The numerical simulation indicates that the excitation amplitudes and the sizes and locations of the concentrated mass have significant impact on the nonlinear response of the buckled beam.