In order to solve practical problems such as kinship storage and inference by computer, based on algebra theory, an algebraic representation model for kinship relations in the Chinese context is proposed. The proposed model first determines the set of relationships to be studied based on the kinship contained in the national standard GBT-4761-2008, and then defines the inverse operation and the binary operation of kinship on this set. Finally, based on this algebraic representation model, a corresponding kinship inference algorithm is proposed. Some unknown kinship relationships can be inferred from known kinship relationships. Compared with the previous kinship inference algorithm, a new representation model is adopted, which can solve more complex problems.