Managers who work in the tourism sector always let satisfying customers' demand be the priority and selecting carrier selection in their passenger transport system is a crucial process. Network reliability is always utilized as a performance index. This study provides a method to identify the ideal carriers according to the relevant network reliability. The network reliability is defined as the probability that a given demand can travel from an origin to a destination within a time limitation. A passenger transport system can be constructed as a flow-network with nodes and arcs linking passengers from the origin (source) to the destination (sink), where each node is a station and each arc represents a bus, a train or a flight connecting two nodes on schedule. Since the contracted carrier of each arc may provide the service to several agents, the capacity of each arc is regarding stochastic with a specific probability. Any flow-network associated with a stochastic capacity is thus a typical stochastic-flow network. This work proposes an algorithm including: evaluate the network reliability under a time constraint of a stochastic-flow passenger transport network, and then employ it as a basis for carrier selection. A case study is also used to demonstrate the selection procedure.