Electronic structures, half-metallic and magnetoelectric properties of pure LiZnN, Mn-doped LiZnN and Mn-doped LiZnN with excess and deficient of Li are geometrically optimized and calculated by using first principle density functional theory based on full potential linearized augumented plane wave method. It reveals that doping of Mn leads to a spin polarized impurity band with a spin polarization of 100%. The system exhibits half-metallic ferromagnetism properties, and strong Mn-N covalent bonds are formed. In Li vacancy system, covalent bonds of Mn-N bonds are strongest. Their bond lengths become shorter, and half-metallic is obviously enhanced. Formation energy of the system decrease, which indicates that the structure is more stable. In Li excess system, half-metallic property of the system disappears and becomes metallic. Impurity band width increases and conductivity of the system increases, but interaction of Mn-N bond becomes weaker. It indicates that magnetic and electrical properties of Mn-doped LiZnN new diluted magnetic semiconductor can be regulated separately via Mn isovalent doping and off-stoichiometry. Ground state of Mn doped LiZnN system is ferromagnetic, and net magnetic moment of the system is mainly contributed by Mn atoms. It is found with Heisenberg model that Li vacancy system increases Curie temperature.