I`ll talk about Cheeger-Gromov L^2 rho-invariant of 3-manifolds. Cheeger and Gromov analytically defined L^2 rho-invariant to Riemannian manifolds and showed L^2 rho-invariant has a universal bound by using deep analytic argument. Chang and Weinberger extended the definition to topological manifolds. Cha proved existence of universal bound for L^2 rho-invariant of topological manifolds and found an explicit bound in terms of a complexity of given 3-manifold. To be specific, L^2 rho-invariant of a 3-manifold can be linearly bounded by a number of 2-handles of a 4-manifold which has a boundary of given 3-manifold. We will discuss about the topological definition and proof about Cheeger-Gromov L^2 rho-invariant of 3-manifolds.