This paper considers a continuous-review inventory system which applies zero-inventory-order (ZIO) replenishment policy and which is subject to supply disruption risk. The supplier’s available and disrupted durations are assumed to follow two independent exponential distributions. A risk-averse manager is likely to overweigh the probability that the supplier is unavailable when the inventory level reaches the reorder point. An inverse-S shaped weighting function is used to describe the manager’s risk-aversion behavior. The supplier’s state transition process is modeled by a two-state continuous-time Markov chain, and the long-run average cost function is constructed according to renewal reward theorems. It is proved that the negative cost function is a unimodal function and that there exists a uniquely optimal inventory order quantity. An approximation method along with an upper bound of the approximated cost function error is proposed which can give the analytic expression for the optimal order quantity. Numerical studies are presented to investigate the biases on optimal order quantities and system costs between risk-averse and risk-neutral managers. Also, with a sample size of 160 benchmark sets and 1 000 random sets, the validity of approximation method is illustrated.