  In this paper, we study the regularity of asymptotically hyperbolic metrics
with Einstein condition near boundary and Weyl curvature smooth enough in
arbitrary dimension. Following Michael Anderson's method, we show that
$C^{m,\alpha}$ conformally compact Riemannian metrics with Einstein equation
vanishing to finite order near boundary have conformal compactifications that
are $C^{m+2,\alpha}$ up to the boundary when Weyl curvature is in
$C^{m,\alpha}$ and the boundary metric is in $C^{m+2,\alpha}$ where $m\geq 3.$
