The self-consistent Theory of Finite Fermi Systems based on the Energy Density Functional byFayans et al. with the set DF3-a of parameters fixed previously is used to calculate three kinds of quadrupolemoments. At first, we examined systematically quadrupole moments of odd neighbors of semi-magic lead andtin isotopes and N = 50, N = 82 isotones. Second, we found quadrupole moments of the first 2+ states in thesame two chains of isotopes. Finally, we evaluated quadrupole moments of odd-odd nuclei neighboring to doublemagic ones. Reasonable agreement with available experimental data has been obtained. Predictions are made forquadrupole moments of nuclei in the vicinity of unstable magic nuclei