This paper considers a vertical structure model where a monopolistic manufacturer and two competitive retailers face a dual channel with online sales, and examines the efficiency of vertical integration. We explain the economic insights on the fundamental trade-off in a dual channel from the viewpoint of transaction cost and investigate social cost in offline and online transactions. Comparing vertical competition models with and without online sales, we show that vertical integration reduces the social cost only when the online cost is sufficiently large. We also show that vertical integration with online channel will reduce channel conflict since integrated firm can share the profits with competitive retailer. However, vertical integration may be inefficient compared to pure online sales when online cost is small. We conclude that an appropriate public policy on vertical integration with online sales should evaluate the efficiency of dual channel based not only on cost replacement effect and web-fit effect, but also on the integration pattern of vertical structure.