We propose privacy-preserving energy management strategies for a microgrid system that consists of several cells and a central control center, with each cell composed of a local controller, a distributed renewable energy generator, and some energy consuming customers. It is assumed that the cells can cooperate by exchanging their locally generated energy and they can obtain external energy, both through the control center. The goal of energy management is to distribute the energy flow within the microgrid system to meet the energy demands of the customers and to minimize the cost of the external energy imported to the system. The problem is formulated as a linear optimization problem with privacy constraints. However, the privacy constraint, i.e., the constraint that the information related to the customers' behaviors in a cell cannot be disclosed to other cells and/or the control center, makes the standard linear programming tools not directly applicable. This motivates us to develop privacy-preserving schemes for effective energy management in such systems. To this end, we develop a dual decomposition-based algorithm and a fast suboptimal algorithm to solve the energy management problem with privacy constraints in a distributed fashion. Simulation results are provided to demonstrate the superior performance of the proposed techniques over the traditional methods.