As an important task of data mining, outlier detection has been applied to many fields. Recently, research on mining in data stream is receiving more and more attention. For solving outlier detection in data stream, a new fast outlier detection algorithm is presented. Based on dynamically grid partitioning data space, the method separates dense areas from sparse areas. Data in dense areas are filtered simply, which reduces greatly the size of objects the algorithm should consider. Outliernesses of candidates in sparse areas are approximated efficiently. Data with high outlierness are outputted as outliers. Results of experiments on synthetic and real data sets show promising availabilities of the approaches.