Dirac cones in the band structure make a great contribution to the unique electronic properties of graphene. But the spin-degeneracy of Dirac cones limits the application of graphene in spintronics. Here, using first-principles calculations, we propose a two-dimensional (2D) metal-organic framework (MOF), Ni2C24S6H12, with spin-polarized Dirac cones at the six corners of the Brillouin zone (BZ). Ferromagnetism is quite stable with a high Curie temperature (630 K) as revealed by Monte Carlo simulation within the Ising model. Taking spin-orbit coupling into account, band gaps are opened up at the Dirac point (5.9 meV) and Γ point (10.4 meV) in the BZ, making Ni2C24S6H12 a Chern topological insulator which is implemented for achieving the quantum anomalous Hall effect. These interesting properties enable Ni2C24S6H12 to be a promising candidate material for spintronics device applications.