  Assume that $(X, g^+)$ is an asymptotically hyperbolic manifold, $(M,
[\bar{h}])$ is its conformal infinity, $\rho$ is the geodesic boundary defining
function associated to $\bar{h}$ and $\bar{g} = \rho^2 g^+$. For any $\gamma
\in (0,1)$, we prove that the solution set of the $\gamma$-Yamabe problem on
$M$ is compact in $C^2(M)$ provided that convergence of the scalar curvature
$R[g^+]$ of $(X, g^+)$ to $-n(n+1)$ is sufficiently fast as $\rho$ tends to 0
and the second fundamental form on $M$ never vanishes. Since most of the
arguments in blow-up analysis performed here is irrelevant to the geometric
assumption imposed on $X$, our proof also provides a general scheme toward
other possible compactness theorems for the fractional Yamabe problem.
