Conceptual design is an early stage in the product design process, which has an essential effect on product innovation. This paper is devoted to computational conceptual design utilizing design synthesis. After the functional model was proposed, the physical parameter model was put forward. The integrated model of function repository and solution repository based on space matrix was built up. The computational conceptual design process based on space matrix was then proposed, including design synthesis algorithm based on space matrix, feature matching based on physical parameter, solutions constraints matching based on design catalog, functional structure design based on functional structure evolutionary model, and evaluation and selection approach based on design catalog. The conceptual design of new devices for decreasing resistance of amphibious vehicles is given as an example, which demonstrates that the methodology is helpful to produce valuable solutions for product innovation.