In this paper, we deal with the learning problem when using an adaptive filtering method. For the learning system in filtering, the knowledge is obtained and updated based on the newly acquired information that is extracted and learned from the sequential samples over time. Effective measurement on the informativeness of a sample and reasonable subsequent treatment on the sample will improve the learning performance. This paper proposes a sequential outlier criterion for sparsification of online adaptive filtering. The method is proposed to achieve effective informativeness measurement of online filtering to obtain a more accurate and more compact network in the learning process. In the proposed method, the measurement on the samples' informativeness is established based on the historical sequentially adjacent samples, and then the informative-measured samples are treated individually by the learning system based on whether the sample is informative, redundant, or abnormal. With our method, a more sensible learning process can be achieved with valid knowledge extracted, and the optimal network in the learning system can be obtained. Simulations based on static function estimation, Mackey-Glass time series prediction, and Lorenz chaotic time series prediction demonstrate that the proposed method can provide more effective classification on samples and more accurate networks in online adaptive filtering.