  Under appropriate assumptions on the $N(\Omega)$-fucntion, the De Giorgi
process is presented in the framework of Musielak-Orlicz-Sobolev space to prove
the H\"{o}lder continuity of fully nonlinear elliptic problems. As the
applications, the H\"{o}lder continuity of the minimizers for a class of the
energy functionals in Musielak-Orlicz-Sobolev spaces is proved; and
furthermore, the H\"{o}lder continuity of the weak solutions for a class of
fully nonlinear elliptic equations is provided.
