A group G is called co-Dedekindian if every subgroup of G is invariant under all central automorphisms of G. In this paper we give some necessary conditions for certain finite p-groups with non-cyclic abelian second centre to be co-Dedekindian. We also classify 3-generator co-Dedekindian finite p-groups which are of class 3, having non-cyclic abelian second centre with |\Omega_1(G^p)|=p.