Altermagnetism, a novel magnetic phase bridging ferromagnetism and antiferromagnetism, exhibits zero net magnetization due to its unique alternating spin arrangements, which cancel out macroscopic magnetization. This phase is characterized by robust time-reversal symmetry breaking and spin-momentum locking, leading to distinct electronic properties advantageous for spintronic applications. In this study, we explore the possibility of altermagnetism in cobalt trifluoride (CoF3) using density functional theory (DFT) with Hubbard U correction combined with spin group theory. Our findings reveal that CoF3 exhibits zero net magnetization similar to a g-type antiferromagnet but with spin degeneracy breaking without spin-orbit coupling, akin to a ferromagnet. The optimized structure of CoF3, characterized by a rhombohedral lattice with centrosymmetric symmetry group R3c, shows significant spin splitting in both valence and conduction bands, reaching up to 45 meV. This spin splitting is attributed to the electric crystal potential and the anisotropy of the spin density, leading to the breaking of Kramers degeneracy.