The electronic structure and magnetic properties of ten formamidinium transition metal iodides in the ground state and under strain have been studied. These formamidinium transition metal iodides have a stable cubic perovskite structure. In the ground state, FAVI3 is a spin gapless semiconductor, and FAScI3, FATiI3, FACrI3, FAFeI3, FACoI3 and FANiI3 are ferromagnetic half-metals. They all have 100% spin polarization and integer total magnetic moment. Under the action of strain, the high spin polarization of some formamidinium transition metal iodides can still be well maintained, and several novel spin gapless semiconductors such as FATiI3, FAFeI3 and FACoI3 have been discovered. Magnetic studies show that these formamidinium transition metal iodides with half-metal, semiconductor and spin-gapless semiconductor properties have integral total magnetic moments under strain ranging from -10.0% to 10.0%. These newly discovered half-metallic ferromagnetic materials and spin gapless semiconductors have broad application prospects in the field of spintronics due to their high spin polarization.