2D half-metallic multiferroic materials have attracted great interest due to their rich novel performances and wide application prospect in nanoelectronics and nanodevices. Three intrinsic half-metallic multiferroic monolayers AV2S4 (A = Na, K, and Rb) are predicted based on the first-principles calculations. From the calculations, their ground states are all ferromagnetic and are completely spin-polarized at the Fermi level. Their total magnetic moments are always 3.00 μB per primitive cell, which origin mainly from V-ions. The two-center electronic structure t2g6↑t2g4↓eg1↑ of V-ions is proposed from the perspective of the crystal field theory to explain successfully the calculated magnetic moments. Interestingly, the alkali-metal ions are non-magnetic, but they may cause important influence on the magnetic coupling between transition ions, and then the half-metallicity of these monolayers. Their electric and magnetic properties may be tuned by their charge states and strains. Especially, their half-metallic stability may be evidently improved by the tensile strains. The half-metallic gaps of these monolayers may be increased by about 67.4%, 50.8%, and 32.4% for NaV2S4, KV2S4, and RbV2S4 by the tensile strain 2.0%, respectively.