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Abstract By mimicking the neurons and synapses of the human brain and employing spiking neural networks on neuromorphic chips, neuromorphic computing offers a promising energy-efficient machine intelligence. How to borrow high-level brain dynamic mechanisms to help neuromorphic computing achieve energy advantages is a fundamental issue. This work presents an application-oriented algorithm-software-hardware co-designed neuromorphic system for this issue. First, we design and fabricate an asynchronous chip called “Speck”, a sensing-computing neuromorphic system on chip. With the low processor resting power of 0.42mW, Speck can satisfy the hardware requirements of dynamic computing: no-input consumes no energy. Second, we uncover the “dynamic imbalance” in spiking neural networks and develop an attention-based framework for achieving the algorithmic requirements of dynamic computing: varied inputs consume energy with large variance. Together, we demonstrate a neuromorphic system with real-time power as low as 0.70mW. This work exhibits the promising potentials of neuromorphic computing with its asynchronous event-driven, sparse, and dynamic nature.