In recent years, intrinsic two-dimensional (2D) magnetism aroused great interest because of its potential application in spintronic devices. However, low Curie temperature (emph{T}$_c$) and magnetic anisotropy energy (MAE) limit its application prospects. Here, using first-principles calculations based on density-functional theory (DFT), we predicted a series of stable MnXSe$_4$ (X=As, Sb) single-layer. The MAE of single-layer MnAsSe$_4$ and MnSbSe$_4$ was 648.76 and 808.95 ${mu}$eV per Mn atom, respectively. Monte Carlo (MC) simulations suggested the emph{T}$_c$ of single-layer MnAsSe$_4$ and MnSbSe$_4$ was 174 and 250 K, respectively. The energy band calculation with hybrid Heyd-Scuseria-Ernzerhof (HSE06) function indicated the MnXSe$_4$ (X = As, Sb) were ferromagnetic (FM) half-metallic. Also it had 100% spin-polarization ratio at the Fermi level. For MnAsSe$_4$ and MnSbSe$_4$, the spin-gap were 1.59 and 1.48 eV, respectively. These excellent magnetic properties render MnXSe$_4$ (X = As, Sb) promising candidate materials for 2D spintronic applications.
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