In oversaturated urban rail transit systems, passengers departing from downstream stations often experience long waiting times due to unbalanced space-time demand and limited transit capacity. This is often prevalent during morning and evening peak periods in transit systems. This paper aims to mitigate the unfairness of waiting time among a time-varying number of passengers through train timetable's adjustment by optimizing the train skip-stopping pattern. We develop an approximate general model by clustering passengers into groups and introducing an aggregation granularity parameter. To characterize feasible passenger travel patterns, both rigid first-in-first-out rule and capacity constraints are incorporated in the proposed model. Preprocessing is proposed to reduce the space of solutions. Some small-scale case studies show that the proposed method outperforms the original timetable and the preprocessing is effective to reduce computation time. Case studies based on the Batong line of Beijing rail transit network are conducted, in which a variable neighborhood search algorithm is applied to obtain high-quality solutions in short computing times. The results show that the proposed approach not only mitigates the unfairness of waiting time among passengers but also improves other efficiency evaluation indexes, including the average waiting time and the maximum number of missed trains. We also investigate the impact of the aggregation granularity parameter on the computational effort and solution accuracy.