To solve the problem of extreme learning machine (ELM) on-line training with sequential training samples, a new algorithm called selective forgetting extreme learning machine (SF-ELM) is proposed and applied to chaotic time series prediction. The SF-ELM adopts the latest training sample and weights the old training samples iteratively to insure that the influence of the old training samples is weakened. The output weight of the SF-ELM is determined recursively during on-line training procedure according to its generalization performance. Numerical experiments on chaotic time series on-line prediction indicate that the SF-ELM is an effective on-line training version of ELM. In comparison with on-line sequential extreme learning machine, the SF-ELM has better performance in the sense of computational cost and prediction accuracy.