Increasing multi-site infant neuroimaging datasets are facilitating the research on understanding early brain development with larger sample size and bigger statistical power. However, a joint analysis of cortical properties (e.g., cortical thickness) is unavoidably facing the problem of non-biological variance introduced by differences in MRI scanners. To address this issue, in this paper, we propose cycle-consistent adversarial networks based on spherical cortical surface to harmonize cortical thickness maps between different scanners. We combine the spherical U-Net and CycleGAN to construct a surface-to-surface CycleGAN (S2SGAN). Specifically, we model the harmonization from scanner X to scanner Y as a surface-to-surface translation task. The first goal of harmonization is to learn a mapping X→Y such that the distribution of surface thickness maps from GX(X) is indistinguishable from Y. Since this mapping is highly under-constrained, with the second goal of harmonization to preserve individual differences, we utilize the inverse mapping Gy:Y→X and the cycle consistency loss to enforce GY (GX(X)) ≈ X (and vice versa). Furthermore, we incorporate the correlation coefficient loss to guarantee the structure consistency between the original and the generated surface thickness maps. Quantitative evaluation on both synthesized and real infant cortical data demonstrates the superior ability of our method in removing unwanted scanner effects and preserving individual differences simultaneously, compared to the state-of-the-art methods.