Support vector machine (SVM) is originally designed for 2-class classification problem under the assumption of independent and identically distributed (i.i.d.) sampling. Most classification problems in practice involve multiple categories, hence the SVM has been extended to handle multi-class classification by solving a series of binary classification problems such as the Directed Acyclic Graph SVM (DAGSVM) method. In this paper, we propose the new DAGSVM based on the Markov sampling to replace the classical framework of i.i.d. samples. Numerical studies on the learning performance of the DAGSVM based on Markov sampling for real-world dátasete are presented. Experimental results indicate that the DAGSVM based on Markov sampling yields better learning performance compared to the DAGSVM algorithm based on independent random sampling.