In this paper, a Meta-cognitive Recurrent Recursive Kernel Online Sequential Extreme Learning Machine with Drift Detector Mechanism (meta-RRKOS-ELM-DDM) is proposed. It combines the strengths of Recurrent Kernel Online Sequential Extreme Learning Machine with a new modified Drift Detector Mechanism (DDM) and Approximate Linear Dependency Kernel Filter (ALD) in solving concept drift problems and reducing complex computations in the learning. The recursive kernel method successfully replaces the normal kernel method in Recurrent Kernel Online Sequential Extreme Learning Machine with DDM (RKOS-ELM-DDM) and generates a fixed reservoir with optimized information in enhancing the forecasting performance. Meta-cognitive learning strategy decides when the incoming data needs to be updated, retrained, or discarded during learning and automatically finding ALD threshold that reduces the learning time of prediction model. In the experiment, six synthetic and three real-world time series datasets are used to evaluate the ability of recursive kernel method, the performance of concept drift detectors, and meta-cognitive learning strategy in time series prediction. Experimental results indicate the meta-RRKOS-ELM with DDM has superior prediction ability in the different predicting horizons as compared with other algorithms.