In this paper we consider how to increase the capacities of the elements in a set E efficiently so that the total cost for the increment of capacity can be decreased to the maximum extent while the final expansion capacity of a given family F of subsets of E is within a given limit bound. We suppose that cost is a stochastic variable which conforms to normal distribution. Network bottleneck capacity expansion problem with stochastic cost is originally formulated as Chance-constrained programming model according to some criteria. In order to solve the stochastic model efficiently, network bottleneck capacity algorithm, stochastic simulation and genetic algorithm are integrated to produce a hybrid intelligent algorithm. Finally, some numerical example are presented