To solve the problem that the hidden layer output of an online sequential extreme learning machine(OS-ELM) algorithm is not stable, the singular matrix is easy to produce, and the OS-ELM has no consideration about the training sample timeliness during the sequential updating process, an improved OS-ELM algorithm online sequential extreme learning machine based on adaptive forgetting factor of kernel function mapping(FFOS-RKELM) is presented based on the regularization and adaptive forgetting factor of kernel function mapping. In the FFOS-RKELM algorithm, the kernel function replaces the hidden layer to produce the stable output results. In the initialization phase, the regularization method can improve the generalization ability of the model by constructing a nonsingular matrix. During the sequential updating phase, the forgetting factor can be adjusted automatically according to new data. The FFOS-RKELM algorithm is applied to the prediction of the chaotic time series and the time series of Inlet NOx. Compared with the OS-ELM algoyithm, the FFOS-RELM algorithm and the OS-RKELM algorithm, the proposed algorithm can improve the prediction accuracy and generalization ability more effectively.