Online sequential extreme learning machine (OS-SELM) is an online learning algorithm training single-hidden layer feedforward neural networks (SLFNs), which can learn data one-by-one or chunk-by-chunk with fixed or varying data size. Due to its characteristics of online sequential learning, OS-ELM is popularly used to solve time-series prediction problem, such as stock forecast, weather forecast, passenger count forecast, etc. OS-ELM, however, has two fatal drawbacks: Its input weights cannot be adjusted and it cannot be applied to learn recurrent neural network (RNN). Therefore we propose a modified version of OS-ELM, called online recurrent extreme learning machine (OR-ELM), which is able to adjust input weights and can be applied to learn RNN, by applying ELM-auto-encoder and a normalization method called Layer normalization (LN). Proposed method is used to solve a time-series prediction problem on New-York City passenger count dataset, and the results show that OR-ELM outperforms OSELM and other online-sequential learning algorithms such as hierarchical temporal memory (HTM) and long short-term memory (LSTM). Furthermore, we applied OR-ELM to anomaly detection problem. We defined absolute percentage error (APE) as an anomaly score, which means how abnormal this input is. Then we also defined an anomaly likelihood using Q-function and the mean of the anomaly score in a time window. Using anomaly likelihood, We can detect anomalies if the anomaly likelihood is near 1. We applied this method to detect anomalies of Koh-Young SPI machine based on its log dataset. We used only the time difference between the logs as OR-ELM’s input features. The result shows that the proposed method successfully detected the anomalies of Koh-Young SPI machine. Furthermore, we applied the OR-ELM to Numenta anomaly benchmark (NAB), to evaluate the performance of the proposed method. The result shows that the OR-ELM ranked 4th plance with the benchmark score of 55.61. This is the result without any optimization method, and its performance can be further increased with proper adaptive method which automatically optimize hyper-parameters in an online manner.