Applying highly accurate neural networks to mobile devices encounters energy problems in battery-limited mobile environments. To resolve these problems, neuromorphic hardware solutions that enable event-driven operation have been proposed. In this work, we present a novel sparse neuromorphic system that implements an E-I Net algorithm to further improve energy efficiency. We introduce a neuron clock-gating technique that significantly reduces energy consumption by predicting future neuron spike activity without any loss of accuracy. We also propose synaptic pruning to save additional energy with minimal impact on classification accuracy. For fast adaptation to a changing environment, a learning algorithm is implemented in the proposed system. Compared to prior studies, our experimental results illustrate that the proposed system achieves 5.3×-11.4× energy efficiency improvement with comparable accuracy.