We have performed a numerical simulation of the three-state vector Potts model on a three-dimensional random lattice. The averages of energy density, magnetization, specific heat and suscetibility of the system in the N× N× N (N = 8, 10, 12) lattices were calculated. These results show that this spin system exhibits an energetie thermal hyoteresis diagram and a sharp peak of specific, which could show that the system experierces phase transition with 1st ordes Z(3) symmetry breaking, this conclusion is supported by the law of the jump of magnetization. These results obtained on the random lattice were consistent with those obtained on the three-dimensional cubic lattices.
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