Motivation: A biochemical reaction, bio-event, depicts the relationships between participating entities. Current text mining research has been focusing on identifying bio-events from scientific literature. However, rare efforts have been dedicated to normalize bio-events extracted from scientific literature with the entries in the curated reaction databases, which could disambiguate the events and further support interconnecting events into biologically meaningful and complete networks. Results: In this paper, we propose BioNorm, a novel method of normalizing bio-events extracted from scientific literature to entries in the bio-molecular reaction database, e.g. IntAct. BioNorm considers event normalization as a paraphrase identification problem. It represents an entry as a natural language statement by combining multiple types of information contained in it. Then, it predicts the semantic similarity between the natural language statement and the statements mentioning events in scientific literature using a long short-term memory recurrent neural network (LSTM). An event will be normalized to the entry if the two statements are paraphrase. To the best of our knowledge, this is the first attempt of event normalization in the biomedical text mining. The experiments have been conducted using the molecular interaction data from IntAct. The results demonstrate that the method could achieve F-score of 0.87 in normalizing event-containing statements.