Mining attractive areas that people interested in and their related movement patterns can lead to instructive insight to transport management, urban planning and location-based services (LBS). The number of visiting that it attracts is used in this paper to measure an area's level of attractiveness (LoA). As one of the most widely used mode of transport, taxi can tell a lot of stories about not only road network traffic condition, but also areas people interested in crossing a day and their related travel patterns, such as travel destination and average travel distance. Conventional taxi trajectory analysis, or more generally, probe vehicle and floating car trajectory analysis, more focuses on road network travel time and average speed estimation. This study from another angle, uses taxi trajectory data to discover attractive areas that people often visit, for instance, hot shopping and leisure places or living and working areas based on their LoA which hereby is represented as the frequency and density of passenger pick-up and drop-off points, because each point represents a certain scope where attractiveness generates. To obtain meaningful patterns, clustering approach is used to group spatiotemporally similar pick-up and drop-off points, because people's interests to these areas varies through time of the day, day of the week, even season of the year. Moreover, a time-dependent travel flow interaction matrix is established, which is a variation of O-D (origin-destination) matrix used in transport domain, and can be used to better understand movement patterns by quantizing the attractiveness among clusters. Background geographic information is used to facilitate the understanding of the movement. This study represents a novel application of taxi trajectory data, reveals people's travel demand and movement patterns in a more deep sense to serve transport management, urban planning, as well as spatiotemporal-tailored location search and services.