  Based on a well-known fact that there are no Einstein hypersurfaces in a
non-flat complex space form, in this article we study the quasi-Einstein
condition, which is a generalization of an Einstein metric, on the real
hyersurface of a non-flat complex space form. For the real hypersurface with
quasi-Einstein metric of a complex Euclidean space, we also give a
classification. Since a gradient Ricci soliton is a special quasi-Einstein
metric, our results improve some conclusions of \cite{CK}.
