To build a power grid fault model which is closer to the actual power grid, a new model named FCA was proposed combined with fuzzy theory and Cellular Automata (CA) to simulate the evolution of power grid failure, and the fuzzy rule bases of cellular status, power status and degree of fault transmission in the model was defined. Meanwhile, simulation with FCA model based on IEEE39 node system was conducted. The simulation results further validate the Self-Organized Criticality (SOC) of power grid, and show that the absolute value of losses load power law curve slope of this model increases by 17% than the model without fuzzy rule, the grid is more stable, and the FCA model is closer to the actual operation of grid.