We propose a new fast purely discriminative algorithm for natural language parsing, based on a "deep" recurrent convolutional graph transformer network (GTN). Assuming a decomposition of a parse tree into a stack of "levels", the network predicts a level of the tree taking into account predictions of previous levels. Using only few basic text features, we show similar performance (in F1 score) to existing pure discriminative parsers and existing "benchmark" parsers (like Collins parser, probabilistic context-free grammars based), with a huge speed advantage.