This paper presents an online learning with regularized kernel based one-class extreme learning machine (ELM) classifier and is referred as online RK-OC-ELM. The baseline kernel hyperplane model considers whole data in a single chunk with regularized ELM approach for offline learning in case of one-class classification (OCC). Further, the basic hyper plane model is adapted in an online fashion from stream of training samples in this paper. Two frameworks viz., boundary and reconstruction are presented to detect the target class in online RKOC-ELM. Boundary framework based one-class classifier consists of single node output architecture and classifier endeavors to approximate all data to any real number. However, one-class classifier based on reconstruction framework is an autoencoder architecture, where output nodes are identical to input nodes and classifier endeavor to reconstruct input layer at the output layer. Both these frameworks employ regularized kernel ELM based online learning and consistency based model selection has been employed to select learning algorithm parameters. The performance of online RK-OC-ELM has been evaluated on standard benchmark datasets as well as on artificial datasets and the results are compared with existing state-of-the art one-class classifiers. The results indicate that the online learning one-class classifier is slightly better or same as batch learning based approaches. As, base classifier used for the proposed classifiers are based on the ELM, hence, proposed classifiers would also inherit the benefit of the base classifier i.e. it will perform faster computation compared to traditional autoencoder based one-class classifier.