The electronic structures, the positron behavior and the positron annihilation lifetimes for void-H, void-He, void-Kr complex in the transitiou metals Ni, Fe, Cr and the noble metal Cu have been calculated, by means of the density functional formalism, the local density approximation based on the jellium model. It is shown that: as the size of the complex increases, the energy levels of bound state of impurity become shallower; and consequently the mean density of scattering state electron inside the complex decreases; and the probability of positron inside the complex and the positron annihilation lifetime inceases.