The DC microgrid is connected to the AC utility by parallel bidirectional power converters (BPCs) to import/export large power, whose control directly affects the performance of the grid-connected DC microgrid. Much work has focused on the hierarchical control of the DC, AC, and hybrid microgrids, but little has considered the hierarchical control of multiple parallel BPCs that directly connect the DC microgrid to the AC utility. In this paper, we propose a hierarchical control for parallel BPCs of a grid-connected DC microgrid. To suppress the potential zero-sequence circulating current in the AC side among the parallel BPCs and realize feedback linearization of the voltage control, a - -0 control scheme instead of a conventional - control scheme is proposed in the inner current loop, and the square of the DC voltage is adopted in the inner voltage loop. DC side droop control is applied to realize DC current sharing among multiple BPCs at the primary control level, and this induces DC bus voltage deviation. The quantified relationship between the current sharing error and DC voltage deviation is derived, indicating that there is a trade-off between the DC voltage deviation and current sharing error. To eliminate the current sharing error and DC voltage deviation simultaneously, slope-adjusting and voltage-shifting approaches are adopted at the secondary control level. The proposed tertiary control realizes precise active and reactive power exchange through parallel BPCs for economical operation. The proposed hierarchical control is applied for parallel BPCs of a grid-connected DC microgrid and can operate coordinately with the control for controllable/uncontrollable distributional generation. The effectiveness of the proposed control method is verified by corresponding simulation tests based on Matlab/Simulink, and the performance of the hierarchical control is evaluated for practical applications.