Quantum field theories based on non-commutative space-time (NCQFT) have been extensively studied recently. However no NCQFT model which can uniquely describe the strong and electroweak interactions has been constructed. This prevents one the make a consistent and systematic study of noncommutative space-time. In this work we construct a NCQFT model based on the triunification gauge group Su(3)c*SU(3)_L*SU(3)_R. A unique feature of this model, that all matter fields (fermions and Higgs bosons) are assigned to (anti-) fundamental representations of the factor SU(3) groups, allows us to construct a NCQFT model for strong and electroweak interactions and their unification without ambiguities. This model provide and example which allows one to make a consistent and systematic study of non-commutative space-time phenomenology, We also comment on some related issues regarding extensions to E_6 and U(3)_L*U(3)_R models.
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