  We investigate the implication of unparticle physics on the B_{u,d}\to (\pi,
K) \pi decays under the constraints of the B_{d,s}-\bar B_{d,s} mixing. We
found that not only the unparticle parameters that belong to the flavor
changing neutral current (FCNC) processes but also scaling dimension d_{\UP}
could be constrained by the B_{d,s}-\bar B_{d,s} mixing phenomenology.
Employing the minimum \chi^2 analysis to the B_{u,d}\to (\pi, K) \pi decays
with the constraints of B_{d,s} mixing, we find that the puzzle of large
branching ratio for B_{d}\to \pi^0 \pi^0 and the discrepancy between the
standard model estimation and data for the direct CP asymmetry of B^+ \to K^+
\pi^0 and B_d \to \pi^+\pi^- can be resolved well. However, the mixing induced
CP asymmetry of B_d\to K_S \pi^0 could not be well accommodated by the
unparticle contributions.
