  We consider the following singularly perturbed nonlinear elliptic problem:
$$-\e^2\Delta u+V(x)u=f(u),\ u\in H^1(\mathbb{R^N}),$$ where $N\ge 3$ and the
nonlinearity $f$ is of critical growth. In this paper, we construct a solution
$u_\e$ of the above problem which concentrates at an isolated component of
positive local minimum points of $V$ as $\e\to 0$ under certain conditions on
$f$. Our result completes the study made in some very recent works in the sense
that, in those papers only the subcritical growth was considered
