We consider the rescaled pure greedy learning algorithm (RPGLA) with the dependent samples drawn according to a non-identical sequence of probability distributions. The generalization performance is provided by applying the independent-blocks technique and adding the drift error. We derive the satisfactory learning rate for the algorithm under the assumption that the process satisfies stationary $\beta$-mixing, and also find that the optimal rate $O(n^{-1})$ can be obtained for i.i.d. processes.