By using first-principles electronic structure calculations, we predict a new two-dimensional half-metallic ferromagnet (2DHMF) with distorted square structure, i.e., the LiCrTe2 monolayer. The results show that the LiCrTe2 monolayer is dynamically, thermally, and mechanically stable, and takes a large in-plane magnetic anisotropy, a wide spin gap, a large magnetization, and a very high Curie temperature. Under a biaxial strain ranging from –5% to +5%, the ferromagnetism, half-metallicity, and high Curie temperature are maintained well. Both tensile and compressive strains can significantly increase the magnitude of the magnetocrystalline anisotropy energy (MAE) and a transition from in-plane easy-x(y)-axis to out-of-plane easy-z-axis occurs when the compressive strain exceeds 1%. Our systematic study of the LiCrTe2 monolayer enables its promising applications in spintronics.