We have studied the superconductivity and structural aspects of substituting Y by Ca in oxygen-deficient YBa2Cu3O7-y (Y:123) high-T-c cuprate superconductor near y approximate to 0.3. Unlike for fully oxygenated systems [1,2], the superconducting transition temperature T-c, determined from AC susceptibility measurements, increases with increasing Ca2+ substitution at the Y3+ Site in this system. A detailed structural analysis of the system has been carried out through neutron diffraction. On replacement of Y by Ca the oxygen content of the Y1-xCaxBa2Cu3O7-y (y approximate to 0.3) system remains nearly unchanged, till x = 0.10, and drops sharply for x = 0.15. The in-plane bond distances in the Cu-O planes decreases with increasing Cu(2)-O(2)-Cu(2) angle, while the bond distances in the Cu-O chains are found to be intact again till x = 0.10. These structural-refinement results indicate that there is an increase in the number of holes with the substitution of Y3+ by Ca2+ in Y1-xCaxBa2Cu3O7-y (y approximate to 0.3) system for x = 0.05 and 0.10. Nearly intact bond distances in the Cu-O chains and decreased Cu(2)-O(2) bond distances in the Cu-O planes indicate that Ca2+ substitution at Y3+ directly dopes the mobile holes in the Cu-O planes without affecting the Cu-O chains for the low level of substitution, i.e., till x = 0.10. The increased number of holes in the system seems responsible for an increase in the T-c of the oxygen-deficient YBa2Cu3O7-y system with Y3+ site Ca2+ substitution. For higher concentration (x = 0.15) of Ca the increased number of holes due to Y3+ by Ca2+ substitution are compensated with a corresponding decrease in oxygen content.