  In this paper we consider a large class of fully nonlinear
integro-differential equations. The class of our nonlocal operators we consider
is not spatial homogeneous and we put mild assumptions on its kernel near zero.
We prove the H\"older regularity for such equation. In particular, our result
covers the case that the kernel $K(x,y)$ is comparable to $|x-y|^{-d-\alpha}
\ln (|x-y|^{-1})$ for $|x-y|<c$ where $0<\alpha<2$.
