Protecting personal privacy and energy efficiency are two primary concerns for mobile ad hoc networks. However, no energy-efficient multicast algorithm designed for preserving anonymity has been proposed to date. At the same time, existing approaches cannot be applied to anonymous routing due to their incapability of preserving anonymity. To solve this critical issue, we propose an energy-efficient anonymous multicast algorithm (EEAMA), which relies only on the statistical properties of the wireless network. This not only makes EEAMA suitable to preserving anonymity, but also reduces its execution time significantly. The complexity of EEAMA increases polynomially with the size of the multicast group, as opposed to the size of the network which determines the complexity of all approaches in the literature. Extensive simulation results show that compared to anonymous unicast, EEAMA offers both better performance (in terms of packet delivery ratio, end-to-end delay and network throughput) and significant energy savings.