In a global economic environment, many enterprises expend their overseas markets and implement outsourcing of logistics activities to external carriers. Many enterprises pay close attention to successful delivery of their freight. Hence, how to determine the optimal carrier selection is a very critical issue for global enterprises. Generally, there are several carriers to serve on each route connecting two cities (or transfer stations) in the logistics network. Each carrier owns multiple available capacities with a probability distribution because the carrier's capacity may be partially reserved for other orders. A carrier selection means selecting 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 a performance index of freight delivery for supply chain management and is defined as the probability that d units of commodity are successfully transmitted from a supplier to a customer. This study focuses on the optimal carrier selection problem based on network reliability criterion. A GA-based algorithm that combines the minimal paths and the recursive sum of disjoint products is developed to determine the optimal carrier selection with the maximal network reliability. A practical logistics example of the LCD monitors delivery from Asia to Europe is presented to illustrate the solution procedure.