  Under general boundary conditions we consider the finiteness of the Hausdorff
and fractal dimensions of the global attractor for the strong solution of the
3D moist primitive equations with viscosity. Firstly, we obtain time-uniform
estimates of the first-order time derivative of the strong solutions in
$L^2(\mho)$. Then, to prove the finiteness of the Hausdorff and fractal
dimensions of the global attractor, the common method is to obtain the uniform
boundedness of the strong solution in $H^2(\mho)$ to establish the squeezing
property of the solution operator. But it is difficult to achieve due to the
boundary conditions and complicated structure of the 3D moist primitive
equations. To overcome the difficulties, we try to use the uniform boundedness
of the derivative of the strong solutions with respect to time $t$ in
$L^2(\mho)$ to prove the uniform continuity of the global attractor. Finally,
using the uniform continuity of the global attractor we establish the squeezing
property of the solution operator which implies the finiteness of the Hausdorff
and fractal dimensions of the global attractor.
