In this paper, a gray GM(1,1) model is used for modeling to realize the construction of differential equations and clustering of prediction errors into different state sets. Then the state transfer matrix is established based on the Markov chain, and the targeted prediction and correction are realized for the interval in which the relative values of the GM(1,1) model are located. For the sequence of random variables, the validity of the method is verified by using the “Marginality” test, and the prediction accuracy of the model is verified by using the residual, posterior difference and correlation tests for the gray prediction model. Finally, a Markov chain-based matching prediction method for traditional music and sports dance is proposed, the overall integration degree is measured, and its prediction matching and integration effects are analyzed. The overall integration degree of sports dance and traditional music was generally between 5.4-8, and the intensity matching coefficient of the common matching method was 100-120, while the intensity matching coefficient of the prediction method using the Markov chain model was 140-160. The actual effect of music-dance matching using the Markov chain model was good and beneficial to the integration of traditional music and sports dance.