Abstract: Enumeration and estimation of bent functions are closely related to the security of stream ciphers designed by them. In this paper, bent matrix is introduced when bent function is denoted by the ordered characteristic matrix. With help of the definition of bent function, some properties of bent matrix are obtained. On the basis of the author's approach to solving the enumeration of the first order correlation-immune Boolean functions, a computable upper bound on the number of bent functions, which is represented by the summation over the integer partition, is given. Examples show that the upper bound is a best possible upper bound.