In view of the fact that Chinese classical poetry and art songs are more and more widely welcomed in people’s entertainment lives, the article conducts research on its market development trend. The PSO-Prophet-LSTM combined prediction model is constructed by combining the Prophet prediction model and the LSTM neural network model and optimizing the combined model with the PSO algorithm. The PSO-Prophet-LSTM model’s prediction performance was tested in this paper and it was used to predict the music industry and the market of Chinese classical poetry and art songs. The PSO-Prophet-LSTM model achieved the best prediction results in terms of the comparison of adaptation, LOSS, and RMSE convergence curves with prediction accuracy. In the prediction of the music industry in the next five years, the total output value of the music industry expanded from RMB 465 billion in 2024 to RMB 986 billion in 2028. The capital preservation rate, the profit tax rate of music output value, and the capital profit rate of the music industry all keep growing over the five years. In the market size prediction of Chinese classical poetry and art songs, the market size of this segment expands with the overall market size of the music industry.