A three-dimensional computational fluid dynamics simulation is performed for a ruby-throated hummingbird (Archilochus colubris) in hovering flight. Realistic wing kinematics are adopted in the numerical model by reconstructing the wing motion from high-speed imaging data of the bird. Lift history and the three-dimensional flow pattern around the wing in full stroke cycles are captured in the simulation. Significant asymmetry is observed for lift production within a stroke cycle. In particular, the downstroke generates about 2.5 times as much vertical force as the upstroke, a result that confirms the estimate based on the measurement of the circulation in a previous experimental study. Associated with lift production is the similar power imbalance between the two half strokes. Further analysis shows that in addition to the angle of attack, wing velocity and surface area, drag-based force and wing–wake interaction also contribute significantly to the lift asymmetry. Though the wing–wake interaction could be beneficial for lift enhancement, the isolated stroke simulation shows that this benefit is buried by other opposing effects, e.g. presence of downwash. The leading-edge vortex is stable during the downstroke but may shed during the upstroke. Finally, the full-body simulation result shows that the effects of wing–wing interaction and wing–body interaction are small.