Transactive control (TC) strategy enhances user engagement in demand response (DR) by incentivizing electricity prices to maintain a balance between supply and demand in the power grid. However, the existing TC strategies are difficult to adapt to the regulation scale of inverter air-conditioning (IA) temperature set-point, and its bidding mechanism lacks motivation for users to participate in DR. To address the above issues, this article proposes a modified transactive control (MTC) strategy. And a virtual-real value mechanism for temperature set-point is introduced in the MTC strategy to overcome the problem of discrete IA temperature set-point. Specially, the variable user desire (UD) is introduced into the bidding mechanism of MTC to encourage users to participate DR. In addition, this study innovatively takes into account users’ willingness to consume thermal comfort and electricity cost. The results of the case analysis show that the proposed MTC strategy can significantly reduce the energy consumption of IA while ensure users’ thermal comfort and electricity cost.