To tackle the dilemma of supporting broadband, high-speed wireless access or well utilizing narrow, non-contiguous spectral resource, Long Term Evolution–Advanced (LTE-A) employs carrier aggregation. It combines different component carriers to send data to users in high rates. Many LTE-A downlink resource scheduling methods seek to assign component carriers or resource blocks to improve throughput or maintain fairness. However, how to save energy spent on communication has not been well studied. Thus, the paper formulates a minimum-energy LTE-A downlink resource scheduling (MARS) problem by using carrier aggregation to allocate resource to users, such that network throughput is improved while energy consumption is reduced. We show that the MARS problem is NP-hard and propose an efficient heuristic by considering data backlog, channel condition, and energy expense of users. Experimental results verify that our heuristic can increase system performance, conserve energy of user equipment, and reduce transmission power emitted from the base station.