In this study, we investigate the proportional fair trajectory design and resource allocation for an unmanned-aerial-vehicle (UAV)-assisted simultaneous wireless information and power transfer (SWIPT) system, where multiple ground nodes (GNs) receive information and harvest energy from the signal transmitted by the UAV using a power-splitting (PS) policy. With this system, we aim to maximize the sum of the logarithmic average spectral efficiency (SE) of the GNs while guaranteeing the average harvested energy requirement to improve the average SE and user fairness simultaneously. To deal with the nonconvexity of the optimization problem, we adopt the quadratic transform and first-order Taylor expansion, proposing an iterative algorithm to find the optimal trajectory and transmit the power of the UAV and the PS ratio of the GNs. Through simulations, we confirm that the proposed scheme achieves a higher average SE compared with the conventional baseline schemes and ensures a level of user fairness similar to that of the state-of-the-art baseline scheme.