In traditional steel–concrete composite beam, the connection between steel beam and concrete slab is ensured by steel shear studs. This paper studies the nonlinear mechanical behavior and failure process of a bonded steel–concrete composite beam by using finite element method. A three-dimensional finite element (FE) model has been developed in this work. The results indicate that there are three major reasons for failure of the composite beam: cracking of the concrete by the local tensile stress, crushing of the concrete by the compressive stress and extensive yielding of the steel beam under the global bending moment.