In this short note we study homogenization of symmetric d-dimensional Lévy processes. Homogenization of one-dimensional pure jump Markov processes has been investigated by Tanaka et al. in [5]; their motivation was the work by Benssousan et al. on the homogenization of diffusion processes in R^d, see also and [11]. We investigate a similar problem for a class of symmetric pure- jump Lévy processes on R^d and we identify - using Mosco convergence - the limit process.