The wide distribution of images of remote sensing (RS) of the Earth in various application areas makes it important to ensure the high quality of such images, which is important to identify necessary information. The complexity of the systems and the impact of various physical processes cause a significant number of distortions that lead to image corruption and possible loss of information. The use of processing methods that should reduce the impact of such factors requires control of their work, which uses quantitative indicators of visual quality. The article considers the task of creating a combined visual quality metric based on an artificial neural network (ANN), which provides high accuracy of visual quality assessment and stability of work on the noise characteristic of the RS. The problem of analysis of RS distortions is considered and the approach of using the database of test images TID2013 for verification on typical RS distortions is offered. The analysis of well-known visual quality metrics and their suitability for the estimation of such images is carried out. According to its results, it was determined that the best metrics provide the accuracy of image quality assessment for RS tasks at the level of 0.93 according to Spearman's rank-order correlation coefficient with subjective estimates of the TID2013 image database. The joint application of existing quality metrics allows eliminating the shortcomings of each of them and increasing the overall efficiency, so the article considers the problems and defines the requirements for creating a combined metric involving a neural network. A method of limiting the number of involved quality metrics with the involvement of Lasso regularization is proposed, which allows determining the most informative features (quality metrics) and simplifying the procedure of selection and reduction of their number. A study was conducted on the influence of the metric selection criterion and quantity on the accuracy of the combined metric. The influence of the structure of the neural network, the number of hidden layers, and the number of neurons in them are also analyzed. Based on the obtained results, the best implementation of ANN was selected, which with the involvement of 16 visual quality metrics allows achieving the accuracy of visual quality assessment at 0.97 according to Spearman's correlation with subjective estimates of the TID2013 database.