One of the main problems of neural network-based no-reference metrics design for image visual quality assessment is small size of image databases with mean opinion scores (MOS). For large networks which can memorize key features of several thousands of images, usage of the databases for metrics training may lead to overlearning. Since data augmentation for image quality assessment is limited by a horizontal image flipping only, the main way to decrease overlearning is to use transfer learning which can significantly speed up training process. In theis paper, we propose a new technique of transfer learning between networks of different architectures using a large set of images without MOS. We implemented the technique for transfer learning between pre-trained KonCept512 metric and a IMQNet metric proposed in this paper. An effectiveness of the transfer learning is estimated in a numerical analysis. It is shown that the trained IMQNet metric provides significantly better correlation with KonCept512 metric (0.89) than other modern metrics. It is also shown that IMQNet pre-trained by the proposed transfer learning shows better correlation with MOS of KonIQ-10k database (0.86) than IMQNet pre-trained using directly the MOS of KonIQ10k (0.73).