As a newly synthesized two-dimensional carbon material, the stability study of monolayer fullerene networks or quasi-hexagonal phase fullerenes (qhp-C₆₀) is timely desirable. We have investigated the stabilities of qhp-C₆₀, including thermal, structural, mechanical, and thermodynamic stabilities, as well as the bonding characteristics, ductility, and mechanical properties, via first-principles calculations. The results show that qhp-C₆₀ is energetically, mechanically, and thermodynamically stable. The thermodynamic stability of qhp-C₆₀ at 300 K and 600 K is verified. The bonding characteristics of qhp-C₆₀ are analyzed from the bond length, and it has sp² and sp³ hybridization. The Pugh ratio (B/G) and Poisson’s ratio (v) indicate similar ductility with graphite and graphene. We also found that qhp-C₆₀ has the lowest hardness and the anisotropy of the material. In addition, the electronic characteristics, including electron localization function (ELF), crystal orbital Hamiltonian population (COHP), and density of states (DOS) at different temperatures, are analyzed to verify the thermal stability of the material. Our results might be helpful in the material design of qhp-C₆₀-related applications.