  Under appropriate assumptions on the $N(\Omega)$-fucntion, the
$L^{\Phi(A(x,\cdot))}$ estimate for the gradient of the minimizers of a class
of energy functional in Musielak-Orlicz-Sobolev space $W^{1,A(x,\cdot)}$ is
presented by using Calder\'{o}n-Zygmund decomposition.
