In this paper, a low complexity algorithm is proposed to improve energy efficiency in LTE networks. Energy efficiency optimization issue is formulated as NP-hard problem which requires high computational cost due to optimal exhaustive search (ES). Then a low complexity energy efficiency optimization algorithm (LCEEO) based on optimal switching-off eNB selection is proposed. With LCEEO, eNBs will be pre-ordered in descending order according to load increments brought into network. First eNB is selected to switch off according to pre-order. Then users in selected eNB will be handed over to other eNBs if quality of service (QoS) for users can be guaranteed. After that, selected eNB is switched off if network energy can be saved. Rest eNBs will be evaluated with updated pre-ordering if any eNB is switched off. Extensive simulations demonstrate that LCEEO can achieve the optimal performance compare to exhaustive search, and the algorithm complexity is significantly reduced.