The effect of the 16 O→ 18 O substitution on the superconducting transition temperatures T c of Na x CoO 2 ⋅yH 2 O has been studied for several sets of samples. Each set has two kinds of samples, one with the oxygen sites in the CoO 2 layers filled with 16 O atoms and another with these sites partially substituted with 18 O isotope. These two kinds of samples were prepared in parallel in whole preparation processes. For all the sample sets, we have not found any significant difference of the T c values between the non-substituted and substituted samples, which indicates that the oxygen isotope effect is not appreciable in Na x CoO 2 ⋅yH 2 O. The result, however, does not necessarily exclude the possibility of the phonon mechanism of the superconductivity, because the strong correlation effect suppresses the isotope effect as pointed out previously.