The acyclic multistate information network (AMIN), which is a kind of MIN that does not require the conservation law of flow, plays an important role nowadays because many modern network structures present AMIN as the construction such as social networks, local area networks (LANs), 4G/5G networks, etc. To effectively evaluate the network reliability of AMIN, which indicates the reliable operation of the network, showing a major and primary metrics for determining the performance and quality of the overall network. The network reliability, which has been shown a NP-hard, has been successfully resolved and approached by the universal generation function method (UGFM). However, the UGFM can only solve small-scale problems due to the overflow in computer memory. To overcome the memory obstacle, an improved and enhanced binary-addition vectors tree algorithm (BAT) is proposed to effectively evaluate and analyze the reliability of AMIN. The performance of the proposed BAT is validated on examples.