This paper considers the generalization ability of two regularized regression algorithms [least square regularized regression (LSRR) and support vector machine regression (SVMR)] based on non-independent and identically distributed (non-i.i.d.) samples. Different from the previously known works for non-i.i.d. samples, in this paper, we research the generalization bounds of two regularized regression algorithms based on uniformly ergodic Markov chain (u.e.M.c.) samples. Inspired by the idea from Markov chain Monto Carlo (MCMC) methods, we also introduce a new Markov sampling algorithm for regression to generate u.e.M.c. samples from a given dataset, and then, we present the numerical studies on the learning performance of LSRR and SVMR based on Markov sampling, respectively. The experimental results show that LSRR and SVMR based on Markov sampling can present obviously smaller mean square errors and smaller variances compared to random sampling.