  Let $X_0$ be an affine variety with only normal isolated singularity $p$ and
$\pi: X\to X_0$ a smooth resolution of the singularity with trivial canonical
line bundle $K_X$. If the complement of the affine variety $X_0\backslash\{p\}$
is the cone $C(S)=\Bbb R_{>0}\times S$ of an Einstein-Sasakian manifold $S$, we
shall prove that the crepant resolution $X$ of $X_0$ admits a complete
Ricci-flat K\"ahler metric in every K\"ahler class in $H^2(X)$. We apply the
continuity method for solving the Monge-Amp\`ere equation to obtain a relevant
existence theorem and a uniqueness theorem of Ricci-flat conical K\"ahler
metrics. By using the vanishing theorem on the crepant resolution $X$ and the
Hodge and Lefschetz decompositions of the basic cohomology groups on the
Sasakian manifold $S$, we construct an initial K\"ahler metric in every
K\"ahler class on which the existence theorem can be applied.We show there are
many examples of Ricci-flat complete K\"ahler manifolds arising as crepant
resolutions.
