This paper analyzes the characteristics of music teaching development, constructs a variety of music integration teaching methods in the background of the “Internet+” era, and evaluates the quality of this teaching method based on the BP neural network algorithm. Since the traditional BP neural network cannot consider modeling the critical point of adjacent teaching quality levels, a Markov chain Monte Carlo simulation with adaptive sampling and BP network is used to study the teaching evaluation problem. Simulation through the constructed evaluation system yields that the prediction accuracy of the model constructed in this paper reaches more than 94%, and the absolute value of the relative error between the predicted and expected results of the model in this paper is controlled within 1.5%. According to this study, teaching the integration of modern pop music and traditional music culture on the Internet is feasible.