The effect of Ca-doping on the superconducting properties of Nd-Ba-Cu-O bulk superconductors, fabricated by the oxygen-controlled melt growth process, has been systematically investigated. Various c-axis textured bulk samples were grown using precursors with the nominal compositions of $Nd_{1.8-x}Ca_{x]Ba_{2.4}Cu_{3.4}O_{y}$ (x= 0.00, 0.02, 0.05, 0.10, 0.15) in a reduced oxygen atmosphere of 1%O$_2$ in Ar. Magnetization measurements revealed that the critical temperatures(Tc) were almost linearly depressed from 95K to 86K with increasing the Ca dopant from x : 0.0 to 0.15, respectively, and thus critical current densities(Jc) at 77K and for H//c-axis of specimens were gradually degraded with increasing x. Compositional analyses revealed that although the amounts of the Ca dopant both in <TEX>$NdBa_2Cu_2O_y(Nd123) and Nd_4Ba_2Cu_2O_{10}(Nd422)$,/TEX> were increased with increasing x, only less than half of the initial Ca compositions were detected in melt-grown Ca-doped Nd-Ba-Cu-O bulk crystals. The supression of Tc is attributed to an increased Nd substitution for the Ba site in the Nd123 superconducting matrix with increasing the amount of the Ca dopant.