We report a study of the decay D0→KS0KS0 using 921~fb−1 of data collected at or near the Υ(4S) and Υ(5S) resonances with the Belle detector at the KEKB asymmetric-energy e+e− collider. The measured time-integrated CP asymmetry is ACP(D0→KS0KS0)=(−0.02±1.53±0.02±0.17)% and the branching fraction is B(D0→KS0KS0) = (1.32 ± 0.02 ± 0.04 ± 0.04) × 10−4, where the first uncertainty is statistical, the second is systematic, and the third is due to the normalization mode (D0→KS0π0) used in the analysis. These results are significantly more precise than previous measurements for this mode. The ACP measurement is consistent with the Standard Model expectation