A task of assessing full-reference visual quality of images is considered. Correlation between the obtained array of mean opinion scores (MOS) and the corresponding array of given metric values allows characterizing correspondence of a considered metric to HVS. For the largest openly available database TID2013 intended for metric verification, a Spearman correlation is about 0.85 for the best existing HVS-metrics. One simple way to improve an efficiency of assessing visual quality of images is to combine several metrics. Our work addresses a possibility of using neural networks for the aforementioned purpose. As leaning data, we have used metric sets for images of the database TID2013 that are employed as the network inputs. Randomly selected half of 3000 images of the database TID2013 has been used at the learning stage whilst other half have been exploited for assessing quality of neural network based HVS-metric. Six metrics “cover” well all types of distortions: FSIMc, PSNR-HMA, PSNR-HVS, SFF, SR-SIM, and VIF, have been selected. As the result of NN learning, the Spearman correlation between the NN output and the MOS for the verification set of database TID2013 reaches 0.93 for the best configuration of NN. This is considerably better than for any particular metric employed as an input (FSIMc is the best among them). Analysis of the designed metric efficiency is carried out, its advantages and drawbacks are demonstrated.