  Let $M$ be a real hypersurface of a complex space form with constant
curvature $c$. In this paper, we study the hypersurface $M$ admitting Miao-Tam
critical metric, i.e. the induced metric $g$ on $M$ satisfies the
equation:$-(\Delta_g\lambda)g+\nabla^2_g\lambda-\lambda Ric=g$, where $\lambda$
is a smooth function on $M$. At first, for the case where $M$ is Hopf, $c=0$
and $c\neq0$ are considered respectively. For the non-Hopf case, we prove that
the ruled real hypersurfaces of non-flat complex space forms do not admit
Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of
a complex Euclidean space admitting Miao-Tam critical metric with $\lambda>0$
or $\lambda<0$ is a sphere and a compact hypersurface of a non-flat complex
space form does not exist such a critical metric.
