Microgrids, as individual controllable entities that can operate either islanded from or interconnected to main power grid, have emerged as a promising solution to improving energy efficiency and resilience to disturbance. When linked together in a self-organized manner, a cluster of microgrids can significantly enhance the reliability and power quality for critical load. With this insight, we study the self-organization and decentralized energy management of a microgrid cluster islanded from main grid after a disruptive event. In the self-organization stage, depending on the available generation resources, each microgrid decides on whether to connect to the cluster; and the microgrid energy management systems then 'negotiate' on the optimal power exchange with each other in the cluster. Once the power exchange is determined, the generation and storage resources of each microgrid are managed to guarantee the energy reliability of critical loads and overall energy efficiency, through a scheduling procedure followed by a dispatch procedure. The effectiveness of the proposed method is revealed via case studies.