This paper addresses a linearized interactive dispatching model developed between active distribution network (ADN) and virtual micro-grid (VMG). To make such concept, a bi-level framework is adopted based on the analytical target cascading (ATC) method. In this model, the lower level dispatches each element in VMG from the standpoint of VMG's own interests, and an objective function of maximizing the VMG's benefits is constructed. The upper level dispatches each element in ADN from the perspective of ADN's economy and reliability, on this basis, a synthetic objective function is built. In addition, the ACT method is used to solve the coupling problem caused by the existence of interaction variables between the upper and lower levels, and ultimately to achieve win-win cooperation between ADN and VMG levels. Moreover, to reduce the computational complexity of the model and speed up the solving process, the secondorder cone programming is employed in the proposed model to linearize the power flow calculation of the distribution network. Finally, simulation studies are conducted on the IEEE 18-bus distribution test systems to illustrate the feasibility of the proposed model. The stability and effectiveness of the model are verified by various comparisons. INDEX TERMS Active distribution network, virtual micro-grid, bi-level model, analytical target cascading, second-order cone programming.