  We calculate the direct $CP$ violation for the decay process of
${B}^{0}\rightarrow \pi^{0}\pi^{0}$, ${B}^{+}\rightarrow \pi^{0}\pi^{+}$,
${B}^{0}\rightarrow K^{0}\pi^{0}$ and ${B}^{+}\rightarrow K^{+}\pi^{0}$ via
isospin symmetry breaking effects from the $\pi^{0}-\eta-\eta'$ mixing
mechanism in perturbative QCD approach. Isospin symmetry breaking originates
from the electroweak interaction and the u-d quark mass difference through the
strong interaction which are known to be tiny. However, we find that isospin
symmetry breaking at the leading order changes the $CP$ violation from the new
strong phases. Our calculation results for the $CP$ violation are within or
including the range of experimental results. We also compare our results with
those from the QCD factorization and the perturbative QCD schemes without
regard to isospin symmetry breaking effects.
