Two-dimensional (2D) intrinsic half-metallic materials are of great interest to explore the exciting physics and applications of nanoscale spintronic devices, but no such materials have been experimentally realized. Using first-principles calculations based on density-functional theory (DFT), we predicted that single-layer MnAsS$_4$ was a 2D intrinsic ferromagnetic (FM) half-metal. The half-metallic spin gap for single-layer MnAsS$_4$ is about 1.46 eV, and it has a large spin splitting of about 0.49 eV in the conduction band. Monte Carlo simulations predicted the Curie temperature (emph{T}$_c$) was about 740 K. Moreover, Within the biaxial strain ranging from -5% to 5%, the FM half-metallic properties remain unchanged. Its ground-state with 100% spin-polarization ratio at Fermi level may be a promising candidate material for 2D spintronic applications.