Broadcast encryption is a cryptographical primitive which is designed for a content provider to distribute contents to only privileged qualifying users through an insecure channel. Anyone who knows public keys can distribute contents by means of public key broadcast encryption whose technique can also be applicable to many other applications. In order to design public key broadcast encryption scheme, it should devise some methods that convert a broadcast encryption scheme based on symmetric key cryptosystem to a public key broadcast encryption. Up to this point, broadcast encryption scheme on trial for converting from symmetric key setting to asymmetric public key setting has been attempted by employing the Hierarchical Identity Based Encryption (HIBE) technique. However, this converting method is not optimal because some of the properties of HIBE are not quite fitting for public key broadcast schemes. In this paper, we proposed new converting method and an efficient public key broadcast encryption scheme Pub-PI which is obtained by adapting the new converting method to the PI scheme [10]. The transmission overhead of the Pub-PI is approximately 3r, where r is the number of revoked users. The storage size of Pub-PI is O($c^2$), where c is a system parameter of PI and the computation cost is 2 pairing computations.