Flexible multi-terminal direct current (MTDC) connection scheme is an ideal way to integrate multiple adjacent microgrids and form interconnected microgrids (IMGs). However, under the traditional control mode, MTDC will lead to frequency/voltage decoupling among all the microgrids. Moreover, improper control scheme design of bidirectional interlinking converters (BICs) in MTDC will make global active/reactive power sharing management impossible, which is considered as the significant task in IMGs. Therefore, a novel distributed cooperative control strategy is designed in this article. In the proposed control strategy, frequency/voltage regulations and local active/reactive power sharing management are achieved through distributed secondary control within each MG. Accurate global active/reactive power sharing management is realized by coordinating the power exchange instructions of each BIC in a distributed manner. The control dynamics of these two levels are designed to be decoupled. The stability of the proposed control strategy is demonstrated by the Lyapunov method, and its effectiveness is verified by simulating a test IMG system in MATLAB/Simulink.