First-principles calculations predict that olivine Li4MnFeCoNiP4O16 has a large toroidal moment and ferrimagnetic configuration with a magnetic moment of 1.99μB per formula unit. Density functional theory pins U (DFT+U) shows an indirect band gap of 0.65 eV in this hypothetical material. The band gap is not simply related to the electronic conductivity when it is used as cathode material in rechargeable Li-ion batteries. Based on the orbital-resolved density of states for the transition-metal ions in the hypothetical material, Co, Ni and Mn are in the high-spin configuration while Fe is in the low-spin configuration, which leads to a large resulting toroidal moment deriving from the Co and Ni ions.The spin configuration of the transition-metal ions in the system breaks the space- and time-inversion symmetry and leads to the magnetoelectric property simultaneously. The ferrotoroidic domain, the fourth form of ferroic, is observed in this new material, as in the case of LiCoPO4 reported recently.