  In this paper we prove that the space $\cM(n,\rv,D,\Lambda):=\{(M^n,g) \text{
closed }: ~~\Ric\ge -(n-1),~\Vol(M)\ge \rv>0, \diam(M)\le D \text{ and }
\int_{M}|\Rm|^{n/2}\le \Lambda\}$ has at most $C(n,\rv,D,\Lambda)$ many
diffeomorphism types. This removes the upper Ricci curvature bound of
Anderson-Cheeger's finite diffeomorphism theorem in \cite{AnCh}. Furthermore,
if $M$ is K\"ahler surface, the Riemann curvature $L^2$ bound could be replaced
by the scalar curvature $L^2$ bound.
