Due to the high connecting strength and excellent load-transferring efficiency, the adhesively stepped-lap composite bonding has been widely used as joints and repairs in advanced aircraft structures. In the service life of composite structures, they frequently subject to bending loads which are rarely reported by the available reference. Hence, in this paper, three-point and four-point bending experiments are performed on composite stepped-lap structures. Typical damage mode of adhesive on the stepped surface has been found in experiments. And the failure of composite fiber, matrix, interlamination and adhesive materials appeared as competitive behavior. Furthermore, numerical models of stepped-lap composite joints, which used cohesive zone model and 3D Hashin criteria to simulate the inter- and intralaminar damages, were utilized to predict the bending strength and progressive damage. The FEM model, based on progressive damage method, captured the detailed failure as the loading displacement was increasing. The simulation results of load displacement and damage have good agreement with the experiments.