Aimed at the possibility of stock-out of the traditional retail channel under stochastic demand in a dual-channel supply chain, we propose a cooperative inventory strategy, in which the excess demand of the traditional retail channel is complemented by the excess inventory of the manufacturer's direct channel through transshipment. We establish a newsboy model to analyse each supply chain member's order quantity decision making process, and prove the unique existence of pure-strategy Nash equilibrium under the uncooperative inventory strategy and the cooperative inventory strategy. We go on to discuss the impacts of the wholesale price, the channel substitution rate and the transshipment cost on optimal order quantities under each inventory strategy. Numerical simulation shows that when values of the wholesale price and the transshipment price satisfy certain conditions, the cooperative inventory strategy can not only lead to an increased supply chain profit but also achieve Pareto improvements of both the manufacturer and the retailer.