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In this paper, a kernel fraction low-power adaptive filtering algorithm based on lncosh function (KFLP-LHCF) is proposed for chaotic time series prediction. The algorithm combines the lncosh function with the kernel fractional low-power algorithm. The nonlinear saturation characteristic of the lncosh function is used to achieve resistance to impulse noise, and the fractional low power is used to suppress the influence of error mutation on the performance of the algorithm. In addition, by adjusting the scale factor, a balance can be achieved between convergence speed as well as steady-state performance. In the alpha noise environment, the proposed algorithm is used to predict and simulate two typical chaotic time series of Lorenz and Mackey–Glass. Experimental results show that the algorithm has better steady-state performance and lower steady-state error than other kernel adaptive filtering algorithms, provided that the convergence speed is similar. [ABSTRACT FROM AUTHOR]