Earlier research on product family design (PFD) often highlights isolated and successful empirical studies with a limited attempt to explore the modeling and design support issues surrounding this economically important class of engineering design problems. This paper proposes a graph rewriting system to organize product family data according to the underpinning logic and to model product derivation mechanisms for PFD. It represents the structural and behavioral aspects of product families as family graphs and related graph operations, respectively. The derivation of product variants becomes a graph rewriting process, in which family graphs are transformed to variant graphs by applying appropriate graph rewriting rules. The system is developed in the language of programmed graph rewriting systems or PROGRES, which supports the specification of hierarchical graph schema and parametric rewriting rules. A meta model is defined for family graphs to factor out those entities common to all product families. A generic model is defined to describe all specific entities relevant to particular families. An instance model describes all product variants for individual customer orders. A prototype of a graph-based PFD system for office chairs is also developed. The system can provide an interactive environment for customers to make choices among product offerings. It also facilitates design automation of product families and enhances interactions and negotiations among sales, design, and manufacturing.