The Information-Centric Network possessing the content-centric features, is the innovative architecture of the next generation of network. Collaborating with fog computing characterized by its strong edge power, ICN will become the development trend of the future network. The emergence of Information-Centric Multimedia Network (ICMN) can meet the increasing demand for transmission of multimedia streams in the current Internet environment. The data transmission has become more delay-constrained and convenient because of the distributed storage, the separation between the location of information and terminals, and the strong cacheability of each node in ICN. However, at the same time, the security of the multimedia streams in the delivery process still requires further protection against wiretapping, interception or attacking. In this paper, we propose the delay-constrained green security communications for ICMN based on chaotic encryption and fog computing so as to transmit multimedia streams in a more secure and time-saving way. We adapt a chaotic cryptographic method to ICMN, implementing the encryption and decryption of multimedia streams. Meanwhile, the network edge capability to process the encryption and decryption is enhanced. Thanks to the fog computing, the strengthened transmission speed of the multimedia streams can fulfill the need for short latency. The work in the paper is of great significance to improve the green security communications of multimedia streams in ICMN.