Abstract: To reduce the computational cost of extreme learning machine (ELM) online training, a new algorithm called local extreme learning machine (LELM) was proposed. LELM adopts the latest training sample and abandons the oldest training sample iteratively to insure that only the most relevant samples are applied to LELM online training. The output weights of LELM are determined recursively during each training procedure to reduce the computational cost of online training. The numerical experiments on chaotic time series prediction indicate that the online training computational cost of LELM is much less than that of ELM. The numerical experiments on radar transmitter condition online monitoring based on time series prediction indicate that LELM has better performance in online training computational cost and prediction accuracy in comparison with conventional electronic system condition online monitoring method using adaptive grey model.