It is critical to design energy-efficient routing protocols for battery-limited mobile ad hoc networks, especially in which the energy-consuming MIMO techniques are employed. However, there are several challenges in such a design: first, it is difficult to characterize the energy consumption of a MIMO-based link; second, without a careful design, the broadcasted RREP packets, which are used in most energy-efficient routing protocols, could flood over the networks, and the destination node cannot decide when to reply the communication request; third, due to node mobility and persistent channel degradation, the selected route paths would break down frequently and hence the protocol overhead is increased further. To address these issues, in this paper, a novel Greedy Energy-Efficient Routing (GEER) protocol is proposed: (a) a generalized energy consumption model for the MIMO-based link, considering the trade-off between multiplexing and diversity gains, is derived to minimize link energy consumption and obtain the optimal transmit model; (b) a simple greedy route discovery algorithm and a novel adaptive reply strategy are adopted to speed up path setup with a reduced establishment overhead; (c) a lightweight route maintenance mechanism is introduced to adaptively rebuild the broken links. Extensive simulation results show that, in comparison with the conventional solutions, the proposed GEER protocol can significantly reduce the energy consumption by up to 68.74%.