Kernel least mean square (KLMS) algorithm is a popular method for time series online prediction. It has the advantages of good robustness, low computational complexity, model simplicity and online learning ability. Unfortunately, as input data grows, the dictionary size increases and the computational complexity raises significantly. In addition, how to improve the adaptability in time-varying environments with noise is also one of the main challenges. Therefore, we propose an improved KLMS algorithm from sparse perspective in response to the above problems, called adaptive sparse quantization kernel least mean square (ASQ-KLMS) algorithm. In the new model, sequential outlier criterion for sparsification and weights adaptive adjustment are combined with coherence criterion and quantization to form ASQ-KLMS algorithm. Firstly, it makes full use of effective information and ignores the interference of abnormal information to obtain a more accurate and compact dictionary. Then, a good balance between algorithm efficiency and accuracy can be achieved by controlling the choice of parameters. In addition, it can adaptively adjust weights in time-varying environment. At last, the Lorenz chaotic time series, the ENSO chaotic time series and the Beijing \(\text {P}{{\text {M}}_{2.5}}\) chaotic time series are used to prove the reliability of the ASQ-KLMS algorithm.