A novel algorithm based on fast leave-one-out cross-validation was proposed, named as online kernel extreme learning machine (OKELM). Online modeling was accomplished by importing the latest training sample and discarding the oldest training sample. An adaptive FLOO-CV prediction error-based threshold without any manual work was used to enhance the sparsity and generalization ability of the model by only introducing the samples with larger predictive error. The output weights of the OKELM were determined recursively based on Hermitian formula. Thus, the online storage space and calculation time was reduced. Numerical experiments on chaotic time series prediction and identification of a continuous stirred tank reactor show that the OKELM has faster calculation speed and higher learning accuracy in comparison with off-line kernel extreme learning machine, unsparsity online kernel extreme learning machine and on-line sequential extreme learning machine.