In this paper we introduce a novel neural network architecture based on Fast Hough Transform layer. The layer of this type allows our neural network to accumulate features from linear areas across the entire image instead of local areas. We demonstrate its potential by solving the problem of vanishing points detection in the images of documents. Such problem occurs when dealing with camera shots of the documents in uncontrolled conditions. In this case, the document image can suffer several specific distortions including projective transform. To train our model, we use MIDV-500 dataset and provide testing results. Strong generalization ability of the suggested method is proven with its applying to a completely different ICDAR 2011 dewarping contest. In previously published papers considering this dataset authors measured quality of vanishing point detection by counting correctly recognized words with open OCR engine Tesseract. To compare with them, we reproduce this experiment and show that our method outperforms the state-of-the-art result.