We examine the effects of an unparticle U as a possible source of missing energy in the p-wave decays of a B meson. The dependence of the differential branching ratio on the K0* (K1) - meson's energy is discussed in the presence of scalar and vector unparticle operators and significant deviation from the standard model value is found after addition of these operators. Finally, we have shown the dependence of the branching ratio for the above-mentioned decays on the parameters of unparticle stuff like effective couplings, cutoff scale Au and the scale dimensions du.