Head-driven phrase structure grammar (HPSG) enjoys a uniform formalism representing rich contextual syntactic and even semantic meanings. This paper makes the first attempt to formulate a simplified HPSG by integrating constituent and dependency formal representations into head-driven phrase structure. Then two parsing algorithms are respectively proposed for two converted tree representations, division span and joint span. As HPSG encodes both constituent and dependency structure information, the proposed HPSG parsers may be regarded as a sort of joint decoder for both types of structures and thus are evaluated in terms of extracted or converted constituent and dependency parsing trees. Our parser achieves new state-of-the-art performance for both parsing tasks on Penn Treebank (PTB) and Chinese Penn Treebank, verifying the effectiveness of joint learning constituent and dependency structures. In details, we report 96.33 F1 of constituent parsing and 97.20\% UAS of dependency parsing on PTB.