The present work is depend upon a different data structure to perform the network reliability estimation efficiently. Zero suppressed binary decision diagram (ZBDD) is an well ordered and effective method of representing not only the boolean functions but also the sets of combinations than the conventional binary decision diagrams (BDD). This paper proposes new algorithm to manipulate the ZBDDs the variant of BDD on some benchmark networks. The 2-terminal network reliability problem has been studied extensively and effective results have been obtained. © 2019, The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden.