Natural disasters can significantly disrupt human mobility in urban areas . Studies have attempted to understand and quantify such disruptions using crowdsourced mobility data sets . However, limited research has studied the justice issues of mobility data in the context of natural disasters . The lack of research leaves us without an empirical foundation to quantify and control the possible biases in the data . This study, using 2017 Hurricane Harvey as a case study, explores three aspects of mobility data that could potentially cause injustice: representativeness, quality, and precision . We find representativeness being a major factor contributing to mobility data injustice . There is a persistent disparity of representativeness across neighborhoods of different socioeconomic characteristics before, during, and after the hurricane's landfall . Additionally, we observed significant drops of data precision during the hurricane, adding uncertainty to locate people and understand their movements during extreme weather events . The findings highlight the necessity in understanding and controlling the possible bias of mobility data as well as developing practical tools through data justice lenses in collecting and analyzing data during disasters.