Extreme learning machine (ELM) has gained increasing attention for its computation feasibility on various applications. However, the previous generalization analysis of ELM relies on the independent and identically distributed (i.i.d) samples. In this paper, we go far beyond this restriction by investigating the generalization bound of the ELM classification associated with the uniform ergodic Markov chains (u.e. M.c) samples. The upper bound of the misclassification error is estimated for the ELM classification showing that the satisfactory learning rate can be achieved even for the dependent samples. Empirical evaluations on real-word datasets are provided to compare the predictive performance of ELM with independent and Markov sampling.