The decay width of the rare decay Z→ν(average) νγγ is strictly constrained from the LEP data. Tensor unparticles provide a tree-level contribution to this rare decay. We have calculated the tensor unparticle contribution to the rare decay Z→ν(average) νγγ. The current experimental limit has been used to constrain the unparticle couplings ν(average) νZU(superscript μν) and γγU(superscript μν).