Half-metallicity, enabling 100% spin polarization, is pivotal for spintronics but remains challenging to achieve in low-dimensional materials. Using first-principles calculations, we theoretically propose an experimentally feasible two-dimensional (2D) metal-organic framework (MOF) magnetic semiconductor, Cr(TCNB)2 (TCNB = 1,2,4,5-tetracyanobenzene). This monolayer can be exfoliated from a Ag(100) substrate due to its low exfoliation energy of 0.14 J/m2. Phonon spectra and ab initio molecular dynamics confirm its dynamical and thermal stability up to 600 K. Cr(TCNB)2 exhibits a ferrimagnetic ground state stabilized by direct p-d magnetic interactions. Notably, carrier doping induces half-metallicity, transforming it into a fully spin-polarized conductor. Monte Carlo simulation predicts that doping elevates the Curie temperature above room temperature. This work introduces a novel 2D MOF magnet with carrier-tunable half-metallicity, offering promising potential for flexible and nanoscale spintronic devices.