Network reliability evaluation for a stochastic flow network (SFN) can be computed in terms of all lower boundary points (LBPs). Although several algorithms have been presented in the literature as solutions for the LBP problem, the efficiency is always occurring at the present for the large SFN. In this paper, a binding technique generating binding-flow vectors is therefore developed to narrow down the searching range of flows for demand. This technique is able to reduce the loading of the candidate comparison procedure greatly. An algorithm based on this binding technique is proposed to solve the LBP problem. We compare the performance of the proposed algorithm to well-known algorithms in terms of CPU time, through three benchmark networks and a practical case. The experimental results show the functional efficiency of our proposed binding LBP algorithm.