Hybrid ac/dc micro-grid is a new concept decoupling dc sources with dc loads and ac sources with ac loads, while power is exchanged between both sides using a bidirectional converter/inverter. This necessitates a supervisory control system to split power between its different resources, which has sparked attention on the development of power management systems (PMSs). In this paper, a robust optimal PMS (ROPMS) is developed for a hybrid ac/dc micro-grid, where the power flow in the micro-grid is supervised based on solving an optimization problem. Satisfying demanded power with maximum utilization of renewable resources, minimum usage of fuel-based generator, extending batteries lifetime, and limited utilization of the main power converter between the ac and dc micro-grids are important factors that are considered in this approach. Uncertainties in the resources output power and generation forecast errors, along with static and dynamic constraints of the resources, are taken into account. Furthermore, since uncertainties in the resources output power may result in fluctuations in the dc bus voltage, a two-level controller is used to regulate charge/discharge power of the battery banks. Effectiveness of the proposed supervisory system is evaluated through extensive simulation runs based on dynamical models of the power resources.