According to the first-principles calculation within PBE+U method and tight-binding model, the magnetic properties and electronic structures of two-dimensional (2D) CrPSe₃ monolayer were investigated. Constructed by a Cr-honeycomb hexagonal lattice, 2D CrPSe₃ was predicted to be in a half-metallic ferromagnetic state with dynamic stability, confirmed by the phonon spectrum with no imaginary dispersion. The Curie temperature was estimated as 224 K by Monte Carlo simulation within the Metropolis algorithm under the periodic boundary condition. The thermal stability of CrPSe₃ monolayer was estimated at 300 K by a first-principles molecular dynamics simulation. It is found that the magnetic ground state of CrPSe₃ monolayer is determined by a competition between the antiferomagnetic d-d direct exchange interactions and the Se-p orbitals mediated ferromagnetic p-d superexchange interactions. Most interestingly, in the half-metallic state the band structure exhibits multiple Dirac cones in the first Brillouin zone: two cones at K point showing a very high Fermi velocityv_\rm F(K) = 15.8 \times 10^5 \;\rm m \!\cdot\! s^-1 about twice larger than the v_\rm F of graphene in the vicinity of Fermi level, and six cones at K'/2 points with v_\rm F (K'/2) = 10.1 \times 10^5\;\rm m \!\cdot\! s^-1 close to the graphene's value. These spin-polarized Dirac cones are mostly composed of Cr \rm d_xz and \rm d_yz orbitals. The novel electronic structure of CrPSe₃ monolayer is also confirmed by the HSE06 functional. A tight-binding model was built based on the Cr-honeycomb structure with two Cr-d orbitals as the basic with the first, second and third nearest-neighboring interactions, further demonstrating that the multiple Dirac cones are protected by the Cr-honeycomb lattice symmetry. Our findings indicate that 2D CrPSe₃ monolayer is a candidate with potential applications in the low-dimensional, high speed and temperature spintronics.