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Under appropriate assumptions on the $N(\Omega)$-fucntion, the De Giorgiprocess is presented in the framework of Musielak-Orlicz-Sobolev space to provethe H\"{o}lder continuity of fully nonlinear elliptic problems. As theapplications, the H\"{o}lder continuity of the minimizers for a class of theenergy functionals in Musielak-Orlicz-Sobolev spaces is proved; andfurthermore, the H\"{o}lder continuity of the weak solutions for a class offully nonlinear elliptic equations is provided.

H\"{o}lder continuity for nonlinear elliptic problem in Musielak-Orlicz-Sobolev space