Network structures and models have been widely adopted, e.g., for Internet of Things, wireless sensor networks, smart grids, transportation networks, communication networks, social networks, and computer grid systems. Network reliability is an effective and popular technique to estimate the probability that the network is still functioning. Networks composed of binary-state (e.g., working or failed) components (arcs and/or nodes) are called binary-state networks. The binary-state network is the fundamental type of network; thus, there is always a need for a more efficient algorithm to calculate the network reliability. Thus, a novel binary-addition tree (BAT) algorithm that employs binary addition for finding all the possible state vectors and the path-based layered-search algorithm for filtering out all the connected vectors is proposed for calculating the binary-state network reliability. According to the time complexity and numerical examples, the efficiency of the proposed BAT is higher than those of traditional algorithms for solving the binary-state network reliability problem.