Groebner basis theory and its computer algorithms have numerous applications inside computer aided design, robotics, cryptosystems and other engineering technique. In this paper we use the difference-differential Gr\"obner bases introduced by Zhou and Winkler (2008) to compute bivariate difference-differential dimension polynomials of difference-differential modules. In cyclic module case, an algorithm for computing bivariate dimension polynomials in difference-differential modules is constructed and verified via the Gr\"obner bases.