Two-dimensional ferromagnetic (2D FM) half-metal holds great potential for quantum magnetoelectronics and spintronic devices. Here, using density functional calculations and magnetic pictures, we study the electronic structure and magnetic properties of the novel van der Waals (vdW) metal-organic framework (MOF), CrCl2(N2C4H4)2, i.e. CrCl2(pyrazine)2. Our results show that CrCl2(pyrazine)2 is a 2D FM half-metal, having a strong intralayer FM coupling but a much weak interlayer one due to the vdW spacing. Its spin-polarized conduction bands are formed by the pyrazine molecular orbitals and are polarized by the robust Cr3+ local spin = 3/2. These results agree with the recent experiments [Pedersen et al., Nature Chemistry, 2018, 10, 1056]. More interestingly, CrCl2(pyrazine)2 monolayer has a strong doping tunability of the FM half-metallicity, and the FM coupling would be significantly enhanced by electron doping. Our work highlights a vital role of the organic ligand and suggests that vdW MOF is also worth exploration for new 2D magnetic materials.