cu-Prolog is an experimental constraint logic programming language. Unlike most conventional CLP systems, cu-Prolog allows user-defined predicates as constraints and is suitable for implementing a natural language processing system based on the unification-based grammar. As an application of cu-Prolog, we developed a JPSG (Japanese Phrase Structure Grammar) parser with the JPSG Working Group (the chairman is Prof. GUNJI, Takao of Osaka University) at ICOT. cu-Prolog is also the complete implementation of the constraint unification and its name (cu) comes from the technique.