In this study, the effects of five fibers on volatile compounds of Korla pear (Pyrus bretschneideri rehd) juice were studied. Four main extraction parameters of headspace solid-phase micro-extraction, namely, sample amount, extraction temperature, extraction time, and salt addition, were optimized for the first time using response surface methodology (RSM) and artificial neural network-genetic algorithm (ANN-GA). The prediction and the generalization ability of RSM and ANN models using the same experimental design were compared. The absolute average deviations of the ANN and RSM models were 0.458 and 0.313, and the correlation coefficients were 0.927 and 0.978, respectively. These results indicated that 65-μm PDMS/DVB fiber is the best extraction fiber of SPME for the volatile compounds of Korla pear juice. The ANN model exhibited more accurate prediction and better generalization capabilities than the RSM model, and the optimum conditions obtained by GA were more accurate than those of RSM. The optimum sample amount, extraction temperature, extraction time, and salt addition were 5.33 g, 45 °C, 25 min, and 11.8% of the amount of SPME of the Korla pear juice sample, respectively. Under the optimum conditions, the content of nine volatile compounds, including propanoic acid ethyl ester, 1-hexanal, butanoic acid ethyl ester, 1-hexanol, (E)-2-hexenal, hexanoic acid ethyl ester, 2-hexenal, 1-nonanal, and acetic acid ethyl ester, was 3.37 ± 0.23 μg/g.