In the case of non-independent and identically distributed samples, we propose a new ueMC algorithm based on uniformly ergodic Markov samples, and study the generalization ability, the learning rate and convergence of the algorithm. We develop the ueMC algorithm to generate samples from given datasets, and present the numerical results for benchmark datasets. The numerical simulation shows that the logistic regression model with Markov sampling has better generalization ability on large training samples, and its performance is also better than that of classical machine learning algorithms, such as random forest and Adaboost.