Water is a basic resource and an essential component of living organisms. It often exhibits some novel properties under confinement. The water clusters (H2O)n (n = 4-8) confined in the cavity of uranyl peroxide cluster Na20(UO2)20(O2)30 (U20) have been computationally investigated by using ab initio molecular dynamics (AIMD) simulations and density functional theory (DFT) calculations in this study. The results show that the confined water clusters can form hydrogen bonds with the internal oxygen atoms (Ouranyl) of U20, and their conformations changed significantly. The average lengths (2.553-2.645 Å) of hydrogen bonds in confined (H2O)n are shorter than those (2.731-2.841 Å) in the corresponding free water clusters. Moreover, these confined hydrogen bonds show better hydrogen bond patterns according to the quantified indices. The natural bond orbital (NBO) calculations determine that there is electron transferring from the U20 to its interior (H2O)n. It is the main reason for enhancing hydrogen bond interactions among the confined water molecules because their oxygen atoms are more negatively charged and their hydrogen atoms are more positively charged. The quantum theory of atoms in molecules (QTAIM) and interacting quantum atoms (IQA) analyses indicate that the confined hydrogen bonds are more covalent, based on the significant electron density ρ(r) and local energy density H(r) at the bond critical points (BCPs), and the stronger energies of interatomic exchange interactions (Vxc). These findings may help to promote the communication of confined water clusters and enrich the understating of confined hydrogen bonds.