  We examine the unparticle CP-conserving phase effects on the direct CP
asymmetry for both polarized and unpolarized lepton in the inclusive $b\to d
\ell^+ \ell^-$ transition, where the flavor changing neutral currents are
forbidden at tree level but are induced by one-loop penguin diagrams. The
averaged polarized and unpolarized CP asymmetries depict strong dependency on
the unparticle parameters. In particular, a sizable discrepancy corresponding
to the standard model is achieved when the scale dimension value is $1<d_{\UP}<
2$. We see that the unparticle stuff significantly enhances, suppresses or
changes the sign of the CP asymmetry depending on the definite value of the
scaling dimension $d_{\UP}$. Especially, when $d_{\UP}\sim 1.1$ the CP
asymmetries vanish.
