Parallel graph reduction is a promising model for new generation computer because of itsamenability to both programming and parallel computing. In this paper, an initial design for a parallel graphreduction model, PGR model, is presented, which employs eager evaluation strategy to exploit conservativeparallelism and provides with primitives and associated tags of nodes to synchronize concurrent tasks .Moreover,a direct operational description of graph reduction in terms of high level instructions (primitives) is given toobtain a virtual machine, called PGRVM. Parallel graph reduction is a promising model for new generation computer because of itsamenability to both programming and parallel computing. In this paper, an initial design for a parallel graphing model, PGR model, is presented, which employs eager evaluation strategy to exploit conservative parallelism and provides with primitives and associated tags of nodes to synchronize concurrent tasks. More over, a direct operational description of graph reduction in terms of high level instructions (primitives) is given toobtain a virtual machine, called PGRVM.