X-ray imaging is a commonly used diagnostic method with important clinical value in chest-disease diagnosis. Exploiting the release of large-scale available datasets, several methods have been proposed for predicting common diseases using chest X-ray images. However, most of the existing predictive models are limited to single-view inputs, ignoring the supportive role of multiview images in clinical diagnosis. Additionally when image features are extracted using a single model, the effective features are incompletely extracted and the accuracy of disease prediction decreases. The present study proposes a new depth-dependent multilevel feature fusion method (DFFM) that combines the visual features of different views extracted via different models to improve the accuracy of disease prediction. DFFM was verified using MIMIC-CXR, the largest available chest X-ray dataset. Experimental results show that the area under the receiver operating characteristic curve was 0.847, 12.6 and 5.3 percentage points higher than the existing single-view and multiview models with simple feature splicing, respectively. These results confirm the effectiveness of the proposed multilevel fusion method.