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Geo-obfuscation is a location privacy protection mechanism used by mobile users to conceal their precise locations when reporting location data, and it has been widely used to protect the location privacy of workers in spatial crowdsourcing (SC). However, this technique introduces inaccuracies in the reported locations, raising the question of how to control the quality loss that results from obfuscation in SC services. Prior studies have addressed this issue in time-insensitive SC settings, where some degree of quality degradation can be accepted and the locations can be expressed with less precision, which, however, is inadequate for time-sensitive SC. In this paper, we aim to minimize the quality loss caused by geo-obfuscation in time-sensitive SC applications. To this end, we model workers’ mobility on a fine-grained location field and constrain each worker’s obfuscation range to a set of peer locations, which have similar traveling costs to the destination as the actual location. We apply a linear programming (LP) framework to minimize the quality loss while satisfying both peer location constraints and geo-indistinguishability, a location privacy criterion extended from differential privacy. By leveraging the constraint features of the formulated LP, we enhance the time efficiency of solving LP through the geo-indistinguishability constraint reduction and the column generation algorithm. Using both simulation and real-world experiments, we demonstrate that our approach can reduce the quality loss of SC applications while protecting workers’ location privacy.