This paper focuses on determining the optimal carrier selection with maximal network reliability for a stochastic logistics network. In a logistics network, there are several carriers to serve on each route connecting two transfer stations. Each carrier owns multiple available capacities with a probability distribution because the carrier's capacity may be partially reserved by other orders. A carrier selection is to determine exact one carrier on each route, and the logistics network according to the carrier selection is thus a stochastic logistic network. The network reliability is defined as the probability that d units of commodity are successfully transmitted from a supplier to a customer. An optimization algorithm which integrates the genetic algorithm, minimal paths and the recursive sum of disjoint products is developed to solve this problem. The solution procedure is discussed by a practical logistics example of the LCD monitors delivery from Asia to Europe.