Abstract: Let G be a complete and separable group with a left invariant metric,and {X(t)} be a homogeneous Levy processes with values in G. By means of operator semigroups we prove:there is a sequence of compound Poisson processes with values in G that converges weakly to {X(t)}.

Key words: Complete separable metric group, Homogeneous Levy Process, Compound Poisson process, Weak convergence