  In this paper, we extend the nontangential maximal function estimate obtained
by C. Kenig, F. Lin and Z. Shen in \cite{KFS1} to the nonhomogeneous elliptic
operators with rapidly oscillating periodic coefficients. The result relies on
the previous work \cite{X2}, and optimal boundary estimates which is based upon
certain estimates on convergence rates. Compared to the homogeneous case, the
additional bootstrap process seems inevitable, and the Neumann boundary
corrector caused by the lower order term are still useful here.
