For the wide dissemination of lung cancer screening by low-dose computed tomography (CT), it is important to determine the optimal conditions for scan and image reconstruction based on objective standards of evaluation. Our aim in this study was to propose a quantitative index of nodule detectability without an observer test. It was essential to determine the apparent size and density of nodules visible on CT images for developing the nodule-detectability index based on a statistical observer-independent method. Therefore, we introduced a computer simulation technique for CT images based on the spatial resolution of the system to evaluate the size and density accurately. By use of scan/reconstruction parameter settings as employed for low-dose CT screening, a detectability index was obtained for target nodules (ideal spheres) of various sizes and with varying contrast (ΔCT) between nodule density and background density. The index was compared with the qualitative results of observer tests of nodule detectability. As the target nodule diameter or ΔCT was increased, the index value increased, implying improved nodule visibility. According to the index, the detection limits for nodules with ΔCTs of 70, 100, or 150 Hounsfield units were approximately 6, 5, and 4 mm in diameter, respectively. Index values were well correlated with nodule detectability as assessed by four observers. The proposed index was effective for quantifying nodule detectability, and its validity was confirmed by an observer test. This index has potential use in the determination of optimal scan/reconstruction parameters for lung cancer screening by low-dose CT without observer test.