Large Language Models (LLMs) have achieved remarkable success with their billion-level parameters, yet they incur high inference overheads. The emergence of activation sparsity in LLMs provides a natural approach to reduce this cost by involving only parts of the parameters for inference. Existing methods only focus on utilizing this naturally formed activation sparsity, overlooking the potential for further amplifying this inherent sparsity. In this paper, we hypothesize that LLMs can learn to be efficient by achieving more structured activation sparsity. To achieve this, we introduce a novel algorithm, Learn-To-be-Efficient (LTE), designed to train efficiency-aware LLMs to learn to activate fewer neurons and achieve a better trade-off between sparsity and performance. Furthermore, unlike SOTA MoEfication methods, which mainly focus on ReLU-based models, LTE can also be applied to LLMs like GPT and LLaMA with soft activation functions. We evaluate LTE on four models and eleven datasets. The experiments show that LTE achieves a better trade-off between sparsity and task performance. For instance, LTE with LLaMA provides a 1.83x-2.59x FLOPs speed-up on language generation tasks, outperforming the state-of-the-art methods.