First-principles calculations were employed to study the solution and diffusion properties of hydrogen (H) at the Si-rich and C-rich $\Sigma$3(111)[1$\overline{1}$0] ($\Sigma 3_{Si}$ and $\Sigma 3_C$) and $\Sigma$9(221)[1$\overline{1}$0] ($\Sigma$9) grain boundaries (GBs) in 3C-SiC. We constructed GBs of varying sizes and calculated their formation energies and excess volumes to identify the stability of GBs. The $\Sigma$9 GB is more stable and has a relatively open structure compared with the $\Sigma$3 GB. The solution energies of H at the $\Sigma 3_{Si}$, $\Sigma 3_C$ and $\Sigma$9 GBs are significantly reduced to 1.46, 2.30 and 1.47 eV, respectively. These values are much lower than that in the bulk. The negative segregation energies indicate that H is more likely to reside at the GBs rather than in the bulk. The diffusion energy barrier of H in the $\Sigma 3_C$ GB is as high as 1.27 eV, whereas in the $\Sigma 3_{Si}$ GB and $\Sigma$9 GB, the barriers are as low as 0.42 eV and 0.28 eV, respectively. These results suggest that H migration will be suppressed in the $\Sigma 3_C$ GB but promoted in the $\Sigma 3_{Si}$ and $\Sigma$9 GBs. The differences in H diffusion behavior among these three GBs may be attributed to the relatively more open structures of the $\Sigma 3_{Si}$ and $\Sigma$9 GBs compared with the $\Sigma 3_C$ GB. These results are essential for understanding the diffusion mechanism of H and its retention behavior in SiC.