It is of practical importance to construct new effective statistical model for discrete and continuous data arising in the real world. The bivariate distribution with FGM copula whose two marginal distributions are normal and geometric, respectively, is proposed. The explicit characteristics and the moment generating function of the distribution are derived. Also, the conditional distributions and their characteristics of the distribution are obtained. The moment and maximum likelihood (ML) estimates for the parameters are investigated and the numerical results for them are presented. Real data analysis that indicates the usefulness of the model is also shown.