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Taxi sharing is a promising approach to reducing energy consumptions, utilizing limited taxi resources efficiently while preserving the interest of individuals. The existing studies mostly fail to locate a pick-up/drop-off point for each individual passenger in scheduling the sharing route. Besides, they can hardly provide personalized services. To this end, we propose a new taxi-sharing system called Flexi-Sharing to provide flexible and personalized taxi sharing services. It considers the nearby alternative pick-up/drop-off locations and schedules a flexible sharing route with the maximum reduced travel distance by letting passengers walk a short distance. For a sharing request, Flexi-Sharing generates the sharing schedule consisting of a set of companions, the shortest sharing route and the best pick-up/drop-off locations by maximizing the satisfaction of involved passengers. Extensive experiments are conducted using a one-month taxi trajectory data collected in Chengdu, China. Experimental results show that Flexi-Sharing achieves 60% sharing rate and reduces 28 000 km travel distances per hour in the city, which are 15% higher and 16% longer than those of the method that delivers passengers at exact requested locations, respectively. Flexi-Sharing also promises a satisfactory system response time and provides superior sharing experiences. [ABSTRACT FROM AUTHOR]