Abstract Data stream is a sequence of data that has unique features. In many data streams, data from one concept is available, and detection of other types of data in data stream is an essential task. One‐class classification is a famous approach to data classification when data from one class is accessible. The principal task of one‐class classification is separating input data in two different parts: target and outlier data. One of the main challenges concerning data classification on the stationary data streams is the response time, which causes negative effects on effective runtime. Most classifiers, that have been proposed on Rd feature space, solve a quadratic problem for classification that leads to extreme runtime increase. In this paper, an incremental one‐class classification on stationary data streams is proposed using two‐quarter sphere (IOCTQ) in order to achieve lower computation cost of classification time, and a linear optimization problem is solved. IOCTQ divides one data classification problem into two data classifiers, and each data point will be individually classified in one‐quarter sphere. The two‐quarter spheres can be run parallel. The results of the experiments have been compared with state‐of‐the‐art methods and show superiority of the IOCTQ method in classification accuracy and time complexity.