Abstract Data-driven Dependency Parsing approaches tend to have low accuracy for Indian languages and Nepali as compared to English and many European languages, which is due to the complex grammatical structures of these languages. Further, due to the unavailability of the universal dependency treebank, validation of any data driven Dependency Parser for the Nepali language is not possible. Therefore, we present a graph and grammar-based dependency parser for Nepali sentences. The parser works in three phases viz. Parts-Of-Speech (POS) tagging which is based on Hidden Markov Model (HMM), rule based Chunking and Dependency Parsing. The parser makes use of the maximal graph matching technique, grammatical knowledge such as verb frames, morphological information and yields the semantically and syntactically correct labeled dependency graphs (parse tree). The parser scores 80.62% on UAS (unlabeled attachment score) and 61.45% on LAS (labeled attachment score) for a random test sample of 2600 sentences.