Purpose To obtain a high-quality finished product model, three-dimensional (3D) printing needs to be optimized. Design/methodology/approach Based on back-propagation neural network (BPNN), the particle swarm optimization (PSO) algorithm was improved for optimizing the parameters of BPNN, and then the model precision was predicted with the improved PSO-BPNN (IPSO-BPNN) taking nozzle temperature, etc. as the influencing factors. Findings It was found from the experimental results that the prediction results of IPSO-BPNN were closer to the actual values than BPNN and PSO-BPNN, and the prediction error was smaller; the average error of dimensional precision and surface precision was 6.03% and 6.54%, respectively, which suggested that it could provide a reliable guidance for 3D printing optimization. Originality/value The experimental results verify the validity of IPSO-BPNN in 3D printing precision prediction and make some contributions to the improvement of the precision of finished products and the realization of 3D printing optimization.