We investigate an unmanned aerial vehicle (UAV)- enabled wireless power transfer (WPT) network. A UAV with a directional antenna array is operated to simultaneously wirelessly transfer energy to multiple ground sensor nodes (SNs). We consider a nonlinear energy harvesting (EH) model and a directional antenna structure of uniform linear array (ULA) where an analog directional beamforming scheme is applied. Taking the fairness issue into account, we formulate a problem aiming at maximizing the minimum harvested energy among all SNs during a fixed time period, via jointly optimizing the UAV trajectory and the orientation of the directional antenna on UAV. Then, we construct a tight convex approximation for the optimization problem, based on which the problem is solved via a proposed iterative algorithm and the objective converges to an efficient suboptimal solution. Finally, we provide numerical results to validate our proposed algorithm and to highlight the benefits of deploying directional antenna in WPT networks.