A data-driven geometric guidance method is proposed for the multi-constrained guidance problem of variable-velocity unmanned aerial vehicles (UAVs). Firstly, a two-phase flight trajectory based on a log-aesthetic space curve (LASC) is designed. The impact angle is satisfied by a specified straight-line segment. The impact time is controlled by adjusting the phase switching point. Secondly, a deep neural network is trained offline to establish the mapping relationship between the initial conditions and desired trajectory parameters. Based on this mapping network, the desired flight trajectory can be generated rapidly and precisely. Finally, the pure pursuit and line-of-sight (PLOS) algorithm is employed to generate guidance commands. The numerical simulation results validate the effectiveness and superiority of the proposed method in terms of impact time and angle control under time-varying velocity.