Characterizing human mobility patterns is essential for understanding human behaviors and the interactions with socioeconomic and natural environment. With the continuing advancement of location and Web 2.0 technologies, location-based social media (LBSM) have been gaining widespread popularity in the past few years. With an access to locations of users, profiles and the contents of the social media posts, the LBSM data provided a novel modality of data source for human mobility study. By exploiting the explicit location footprints and mining the latent demographic information implied in the LBSM data, the purpose of this paper is to investigate the spatiotemporal characteristics of human mobility with a particular focus on the impact of demography. We first collect geo-tagged Twitter feeds posted in the conterminous United States area, and organize the collection of feeds using the concept of space-time trajectory corresponding to each Twitter user. Commonly human mobility measures, including detected home and activity centers, are derived for each user trajectory. We then select a subset of Twitter users that have detected home locations in the city of Chicago as a case study, and apply name analysis to the names provided in user profiles to learn the implicit demographic information of Twitter users, including race/ethnicity, gender and age. Finally we explore the spatiotemporal distribution and mobility characteristics of Chicago Twitter users, and investigate the demographic impact by comparing the differences across three demographic dimensions (race/ethnicity, gender and age). We found that, although the human mobility measures of different demographic groups generally follow the generic laws (e.g., power law distribution), the demographic information, particular the race/ethnicity group, significantly affects the urban human mobility patterns.