In statistics copulas study and their applications are growing field which are very efficient functions in statistics and specially in statistical inference. Copula is used for constructing families of bivariate and multivariate distributions and a way of studying measure of dependence structure also, this copula couple multivariate distribution functions to their one-dimensional marginal distribution functions, which are uniformly distributed in [0,1]. They are several methods for constructing copulas as inverse method, Rüschendorf’s method, geometric method, algebraic method, and Archimedean method hence, we construct new copula according to univariate function. Copulas have appeared in many important fields such as civil engineering, biomedical studies, physics, quantitative finance, economics, climatology, social science, and insurance risk management which confirms its importance. This paper introduces some bivariate copulas as product, Clayton, Frank, Ali-Mikhail-Haq, Farlie-Gumbel-Morgensten, and Gumbel-Hougaard copulas. A new class of bivariate copula is introduced which depending on a univariate function. The basic properties which satisfied that is a true copula namely, the boundary conditions and the 2-increaing property are proved. Several properties of this class are studied as concordance ordering, dependence, symmetry, and measures of association. Further, example is proposed generated by a univariate function that described parametric family of copula as product copula.