This paper constructs a multistate distribution network (MDN) under the delivery spoilage consideration and then evaluates network reliability for the MDN. An MDN is composed of nodes and routes, where each node denotes a supplier, a transfer center, or a market, and each route connects a pair of nodes. Along each route, there is a carrier whose available capacity is stochastic. Moreover, goods may rot or be spoilt during delivery due to traffic accidents, collisions, natural disasters, weather, time, etc., and thus the intact goods may not satisfy the market demand. Network reliability is defined as the probability that the MDN can satisfy the market demand under the delivery spoilage consideration and the delivery budget constraint, and can be regarded as a performance index for distribution activity in supply chain management. An algorithm is developed in terms of minimal paths to evaluate network reliability. Then a practical case of fruit distribution is presented to illustrate the solution procedure.