Electronic, magnetic and elastic calculations of a new Ti2RuTl full Heusler compound have been made using the Vienna Ab-initio Simulation Package (VASP). The computations were carried out for the ferromagnetic (FM) state in the F-43 m (No.216) space group. Ground-state values of the lattice parameter, bulk modulus, volume and energy were obtained. The lattice parameter of the cubic structure was 6.478 angstrom. According to the electronic calculations, the spin-up electrons were found to have metallic properties while the spin-down electrons were found to have a semiconductor nature. Therefore, these metallic and semiconductor spin states showed that the Ti2RuTl full Heusler compound is a half-metallic (HM) ferromagnet with 1.00 mu(B)/f.u. magnetic moment. Finally, the elastic calculations showed that the compound is an elastically stable, ductile material and could be a new candidate material for using in spintronics.