The flight performance and efficiency of a bionic dragonfly flapping-wing vehicle are influenced by unsteady flight parameters. Parameter optimization is required to improve aerodynamic characteristics. A relative motion model of bionic dragonfly wings was established based on the flapping-wing flight mechanism. Numerical simulations were performed using Xflow software. The lift, drag, and flow-field evolution were investigated under different stroke-reversal angles and flapping angles. Lift increases with increasing stroke-reversal angle. When the stroke-reversal angle increases from 30° to 90°, the mean lift increases from 0.06 N to 0.96 N. The mean drag decreases slightly from -0.36 N to -0.57 N, corresponding to a relative reduction of approximately 58.3%. Lift also increases with increasing flapping angle. When the flapping angle increases from 60° to 120°, the mean lift increases from 0.27 N to 0.89 N, with a relative increase of approximately 229.6%. Drag decreases as the flapping angle increases, and the mean drag decreases from -0.24 N to -0.93 N, corresponding to a relative reduction of approximately 287.5%. High-pressure regions are formed on the lower wing surface during the downstroke and on the upper surface during the upstroke. The evolution of unsteady vortex structures governs the flow-field development and the time-varying lift and drag characteristics. An appropriate increase in stroke-reversal angle and flapping angle improves the aerodynamic performance of the bionic dragonfly flapping-wing vehicle. The results provide reference data for the aerodynamic design of bionic flapping-wing systems.