A genetic algorithm for supporting architectural conceptual design is presented in this paper. The algorithm adopts mathematical expression binary tree based coded approach, corresponding crossover and mutation operations, and the combination of objective function and interaction with designers for getting fitness values to generate simple curves. The selected shapes are dealt with via 3D visualizing technology to form entities. These generative 3D entities are put together with components designed by designers, then are classified and saved in a component database. The complex configuration design is implemented via combination of different components that come from component base while the combinational scheme is formed by binary coded genera tic algorithm. The process of algorithm is illustrated by an architectural design example.