The mixing of $K^0-bar{K^0}$, $D^0-bar{D^0}$ and $B_{(s)}^0-bar{B^0_{(s)}}$ provides a sensitive probe to explore new physics beyond the Standard Model. The scale invariant unparticle physics recently proposed by Georgi can induce flavor-changing neutral current and contribute to the mixing at tree level. We investigate the unparticle effects on $B^0-bar{B^0}$ and $D^0-bar{D^0}$ mixing. Especially, the newly observed $D^0-bar{D^0}$ mixing sets the most stringent constraints on the coupling of the unparticle to quarks.
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