This paper proposes a hierarchical control scheme based on distributed alternating direction method of multipliers (ADMM) for the interconnected DC microgrids cluster. This scheme is fully distributed and consists of three coordinated control levels through bi-level distributed communication networks. The constraints of the economic dispatch problem are decoupled for tertiary control and decomposed into global and local optimization problems using the ADMM framework. To realize parallel computing of ADMM, we designed a fast second-order distributed average consensus algorithm to estimate the global average exchanged value and the average output power of a single microgrid, thus removing the coupling within the microgrids cluster and individual microgrid. Considering the voltage deviation caused by the traditional droop control, voltage control without droop based on the distributed algorithm is proposed to realize voltage restoration and power distribution among dispatchable generators for individual microgrid, combined with traditional primary and secondary control. Numerical simulations of an off-grid microgrids cluster are designed to validate the effectiveness of the proposed control method. Results show that the proposed hierarchical control scheme can ensure the independence and privacy of information, which is beneficial to solve technical and economic challenges brought by centralized optimization. In addition, the proposed algorithm can be applied to more realistic scenarios, such as conditions for time-varying loads and cost functions.