Recently, a novel [2+2] cycloaddition between the classical Ih-C60 and a fluorenylideneallene complex has been achieved experimentally. In the fullerene-fluorene dyad product, stereo- and regio-selectivities were found in the experiment, but the reasons are still unknown. Our theoretical studies suggest that, based on a diradical pathway, the structural selectivity of the product strongly depends on the structural/electronic features of the fluorenylideneallene and C60 complexes. When the R1 group in fluorenylideneallene denotes the H atom, the E-type product is more stable than the Z-type one, whereas other bulkier R1 groups lead to the reverse due to their steric hindrance. The π orbital conjugation between the fluorenyl group and the Cβ═Cγ bond in fluorenylideneallene is the main reason for the high selectivity of β,γ-cycloaddition. Analyses of both frontier orbitals and spin density for the intermediate structure suggest a diradical pathway of the reaction between fluorenylideneallene and C60 and uncover a decisive role of the LUMO of C60 toward regio-selectivity, which conduces to a high selectivity of the (6,6)-addition product.