In a hierarchical structure, a user in a security class has access to information items of another class if and only if the former class is a predecessor of latter. Based upon cryptographic techniques, several schemes have been proposed for solving the problem of access control in hierarchical structures. In this paper, we propose a new scheme for an access control in tree structural hierarchies based on asymmetric cryptographic key assignment scheme. Further, our encryption and decryption procedures are based on asymmetric cryptographic technique. We show that proposed scheme requires less amount of storage space to store public parameters and also retains the same security level compared to the previous published schemes. Furthermore, our scheme achieves better generality compared to the Hwang’s scheme.