We consider periodic homogenization problems for Lévy operators with asymmetric Lévy densities. The formal asymptotic expansion used for the α-stable (symmetric) Lévy operators (α ∈ (0, 2)) is not directly applicable to such asymmetric cases. We rescale the asymmetric densities and extract the most singular parts of the measures, which average out the microscopic dependencies in the homogenization procedures. We give two conditions, (A) and (B), that characterize such a class of asymmetric densities under which the above ‘rescaled’ homogenization is available.