We investigate the implication of unparticle physics on the Bu,d→(π,K)π decays under the constraints of the Bd,s–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 dU could be constrained by the Bd,s–B¯d,s mixing phenomenology. Employing the minimum χ2 analysis to the Bu,d→(π,K)π decays with the constraints of Bd,s mixing, we find that the puzzle of large branching ratio for Bd→π0π0 and the discrepancy between the standard model estimation and data for the direct CP asymmetry of B+→K+π0 and Bd→π+π− can be resolved well. However, the mixing induced CP asymmetry of Bd→KSπ0 could not be well accommodated by the unparticle contributions.