The dipole polarizabilities of the 1, 2(1)S and 2(3)S states of helium-like ions (2 less than or equal to Z less than or equal to 10) are calculated through a variation-perturbation approach. The polarized wavefunctions are constructed by using selecting B-spline basis functions in a CI scheme. The values of alpha(d) are converged to an accuracy of at least 0.01% and are in excellent agreement with those obtained from explicitly correlated wavefunctions and with experiment (Leonard and Barker).