In this study, we focus on the feasibility of structural topology optimization for a steel-timber composite beam design of optimally allocating glue-laminated timbers into a web with openings under the condition of given steel flanges. The motivation of this study is to topologically take maximal stiffness harmonizing both tension and compression performance of the steel-timber composite beam and become the eco-frandly timber design for buidling members. As a result of this study, the key web-openings allocation becomes triangle spaces, i.e., empty or no materials, of optimal topologies of both a pure timber plate and a steel flange-web timber plate without web-openings. Several applicable examples verify the effectiveness of topology optimization for steel-timber beams with web-openings.