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The existing Petri Net researches of production system always define the trigger rates as some certain values. The problems can bring some risks or mistakes to analysis, evaluation and prediction of system performance, causing the managers hard to make the right, proper and efficient production plans and decisions. According to this, writers introduce Grey System theory into Petri Net, setting some uncertain trigger rates as interval grey numbers, firstly defining Grey Petri Net theory and designing its modeling, algorithm and analysis methods. At last, the writers establish a Grey Petri Net model to illustrate its algorithms and analysis methods, making some analysis and the evaluation of System Performances as machine utilization, productivity and system cycle time, get a good effect.