Abstract: A spectral geometry-incremental harmonic balance method （SGM-IHBM） is proposed to study the nonlinear vibration characteristics of functionally graded porous （FGP） beams with geometric nonlinearities. The geometrically nonlinear strain-displacement relationship of the beam structure is obtained according to the Von-Karman theory， and the Lagrange energy function of the FGP beam is derived based on the Timoshenko theory. The spectral geometric series are used to characterize each displacement component of the beam structure， and the linear modal components are introduced to establish the nonlinear reduced-order equations of the FGP beams， and then the incremental harmonic balance （IHB） method is used to trace the dynamical response solution of the reduced-order model of the FGP beams. The correctness of the nonlinear model in this paper is verified by comparing the SGM-IHBM solution with the literature solution， and then the effects of porosity， thickness， and excitation amplitude on the nonlinear vibration characteristics of FGP beams are analyzed.