We compute to next-to-leading order in QCD the tensor unparticle contribution to the diphoton production at the LHC, wherein the unparticle sector is a consequence of (a) scale invariance but not full conformal invariance and (b) conformal invariance. We use the semianalytical two cutoff phase-space slicing method to handle the O(αs) corrections to the pp→γγX and show that our results are insensitive to the soft and collinear cutoffs. In order to avoid the contribution of the photons due to fragmentation, we employ the smooth cone isolation criterion. Significance of the QCD corrections to the diphoton events including unparticles is highlighted. © 2009 The American Physical Society.