Computed tomography (CT) chest scans have become commonly used in clinical diagnosis. Image quality assessment (IQA) for CT images plays an important role in CT examination. It is worth noting that IQA is still a manual and subjective process, and even experienced radiologists make mistakes due to human limitations (fatigue, perceptual biases, and cognitive biases). There are also kinds of biases because of poor consensus among radiologists. Excellent IQA methods can reliably give an objective evaluation result and also reduce the workload of radiologists. This study proposes a deep learning (DL)-based automatic IQA method, to assess whether the image quality of respiratory phase on CT chest images are optimal or not, so that the CT chest images can be used in the patient's physical condition assessment. This retrospective study analysed 212 patients' chest CT images, with 188 patients allocated to a training set (150 patients), validation set (18 patients), and a test set (20 patients). The remaining 24 patients were used for the observer study. Data augmentation methods were applied to address the problem of insufficient data. The DL-based IQA method combines image selection, tracheal carina segmentation, and bronchial beam detection. To automatically select the CT image containing the tracheal carina, an image selection model was employed. Afterward, the area-based approach and score-based approach were proposed and used to further optimize the tracheal carina segmentation and bronchial beam detection results, respectively. Finally, the score about the image quality of the patient's respiratory phase images given by the DL-based automatic IQA method was compared with the mean opinion score (MOS) given in the observer study, in which four blinded experienced radiologists took part. The DL-based automatic IQA method achieved good performance in assessing the image quality of the respiratory phase images. For the CT sequence of the same patient, the DL-based IQA method had an accuracy of 92% in the assessment score, while the radiologists had an accuracy of 88%. The Kappa value of the assessment score between the DL-based IQA method and radiologists was 0.75, with a sensitivity of 85%, specificity of 91%, positive predictive value (PPV) of 92%, negative predictive value (NPV) of 93%, and accuracy of 88%. This study develops and validates a DL-based automatic IQA method for the respiratory phase on CT chest images. The performance of this method surpassed that of the experienced radiologists on the independent test set used in this study. In clinical practice, it is possible to reduce the workload of radiologists and minimize errors caused by human limitations.