The static quadrupole polarizabilities for hydrogen-like ions from Z =1 to Z =100 in the 1S1/2 ground state are calculated to high precision by solving the Dirac equation using the B-spline Galerkin method.The results are consistent with the expression of Kaneko [J.Phys.B 10 (1977) 3347] at low Z.The quadrupole oscillator strength sum Σn f(2)gn is computed to be zero to a very high degree of precision.