The previously known frameworks describing the consistency of support vector machine classification (SVMC) algorithm are usually based on the assumption of independent and identically distributed (i.i.d.) samples. In this paper we go far beyond these classical frameworks by studying the consistency of SVMC algorithm with uniformly ergodic Markov chain samples based on linear prediction models. We establish the bound on the consistency of SVMC algorithm with uniformly ergodic Markov chain samples, and show that SVMC algorithm with uniformly ergodic Markov chain samples is consistent. Inspired by the idea from Markov chain Monto Carlo (MCMC) methods, we introduce a new Markov sampling algorithm for classification to generate uniformly ergodic Markov chain samples from large data set, and present numerical studies on simulated data and benchmark repository using SVMC algorithm.