By using density functional theory calculations combined with statistical thermodynamic analyses, the stabilization performance of a series of fullerene cages C2n (2n = 70-74) via encapsulating monometal uranium was systematically and thoroughly investigated. Results indicate that fullerene cages D5h(8149)-C70 and D3h(14246)-C74 obeying the isolated pentagon rule and C2(10612)-C72 featured with one pentalene moiety were the most promising candidates to encage uranium. Subsequent Mulliken spin density distribution and frontier molecular orbital analyses suggest that four formal electron transfer occurs from monometal U to above the carbon cages. There also exists a high degree of covalent character between the atom U and fullerenes C2n based on Mayer bond order and quantum theory of atoms in molecule (QTAIM) analyses, indicative of the cooperative stabilization by both ionic and covalent bonding interactions. In addition, investigations on the above-mentioned U@C2n isomers and other favorable candidates (U@Cs(8094)-C70, U@C1(10610)-C72, U@C1(13393)-C74, and U@C1(14049)-C74) reveal that these isomers could be closely linked via simple C2 addition and Stone-Wales transformation. These results will provide a systematic understanding on U-based endohedral metallofullerenes (EMFs) and also might be helpful for further exploration of EMF growth mechanisms.