Thermal printing is a prevalent method due to its advantages of rapid output, cost effectiveness, and ease of use. However, the quality of thermal printing is influenced by the printing speed, the temperature, and the concentration and characteristics of the materials. This research employs a BP neural network to forecast print quality, utilizing two activation functions. The findings indicate that a dual-layer hidden configuration utilizing the GeLU activation function yields a lower root-mean-square error (RMSE). The optimal configuration identified consists of six neurons in the first hidden layer and three neurons in the second hidden layer. To enhance the predictive performance, a PSO algorithm was integrated with the PSO-BP model to refine the parameter selection, which included ambient temperature, printing speed, and printing concentration, with iterative training and validation conducted via the gradient descent algorithm. The PSO-BP network achieved an MAE of 0.1108, an RMSE of 0.145, an MSE of 0.021, and an R² value of 0.9916 in predicting print quality. These results substantiate the stability and reliability of the neural network model developed with the PSO algorithm. Further validation with ten sets of test samples demonstrated that the model attained an average absolute error of 2.77% in print quality predictions, indicating robust generalization capabilities and precise forecasting.