Copula function has been widely used in insurance and finance for modeling inter-dependency between risks. Inspired by the Bernstein copula put forward by Sancetta and Satchell (2004, Econometric Theory, 20, 535–562), we introduce a new class of multivariate copulas, the composite Bernstein copula, generated from a composition of two copulas. This new class of copula functions is able to capture tail dependence, and it has a reproduction property for the three important dependency structures: comonotonicity, countermonotonicity and independence. We introduce an estimation procedure based on the empirical composite Bernstein copula which incorporates both prior information and data into the estimation. Simulation studies and an empirical study on financial data illustrate the advantages of the empirical composite Bernstein copula estimation method, especially in capturing tail dependence.