The aim of this study was to examine the performance of a convolutional neural network (CNN) combined with exponentiating each pixel value in classifying benign and malignant lung nodules on computed tomography (CT) images. Images in the Lung Image Database Consortium-Image Database Resource Initiative (LIDC-IDRI) were analyzed. Four CNN models were then constructed to classify the lung nodules by malignancy level (malignancy level 1 vs. 2, malignancy level 1 vs. 3, malignancy level 1 vs. 4, and malignancy level 1 vs. 5). The exponentiation method was applied for exponent values of 1.0 to 10.0 in increments of 0.5. Accuracy, sensitivity, specificity, and area under the curve of receiver operating characteristics (AUC-ROC) were calculated. These statistics were compared between an exponent value of 1.0 and all other exponent values in each model by the Mann-Whitney U-test. In malignancy 1 vs. 4, maximum test accuracy (MTA; exponent value = 2.0, 3.0, 3.5, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, and 10.0) and specificity (6.5, 7.0, and 9.0) were improved by up to 0.012 and 0.037, respectively. In malignancy 1 vs. 5, MTA (6.5 and 7.0) and sensitivity (1.5) were improved by up to 0.030 and 0.0040, respectively. The exponentiation method improved the performance of the CNN in the task of classifying lung nodules on CT images as benign or malignant. The exponentiation method demonstrated two advantages: improved accuracy, and the ability to adjust sensitivity and specificity by selecting an appropriate exponent value. Adjustment of sensitivity and specificity by selecting an exponent value enables the construction of proper CNN models for screening, diagnosis, and treatment processes among patients with lung nodules. • The exponentiation method improved the performance of the convolutional neural network. • Contrast accentuation by the exponentiation method may derive features of lung nodules. • Sensitivity and specificity can be adjusted by selecting an exponent value.