An FeCl2 monolayer is a half-metallic two-dimensional (2D) magnetic material, which has been investigated theoretically from different perspectives. In this paper, the electronic properties of the stable half-metallicity of a 2D trigonal FeCl2 nanosheets under external stress, magnetic modulation of electronic structures of quasi one-dimensional (1D) trigonal FeCl2 nanoribbons were calculated by the first-principle method. The calculated band structures show that the half-metallicity of a 2D trigonal FeCl2 nanosheet is dynamically stable and isotropic, and its half-metallicity is always presented in different structures as stress gradually increases along the armchair and zigzag directions. Meanwhile, the spin-dependent band structures of quasi-1D trigonal FeCl2 nanoribbons with diverse boundaries and distinct magnetic states show metallic, half-metallic or semiconductor characteristics. Most nanoribbons we considered were half-metallic in the ferromagnetic state, except for the nanoribbons with a width of 10 and both edges bounded by Cl atoms, which were metallic. Depending on nanoribbon width, the nanoribbons with Cl atoms on both edges showed semiconducting behavior along with oscillating band gaps in the nonmagnetic state, and metallic or half-metallic behavior in the antiferromagnetic state. The total energies revealed that the ferromagnetic state was the ground state of the FeCl2 nanoribbons with Cl on both edges. These extraordinary electronic structures indicate the promise of trigonal FeCl2 for use in spintronic devices.