Spintronic devices utilize the electron charge and spin degree of freedom to achieve novel quantum functionalities. Diluted magnetic semiconductors (DMS) constitute an important category of spintronic materials that have the potential to be successfully incorporated into the existing semiconductor industry. The prototypical DMS (Ga,Mn) As, discovered in the 1990s, accomplishes spin and charge doping simultaneously through the heterovalent substitution of the magnetic ion Mn2+ for Ga3+. Two challenges have presented themselves in this material. First, the heterovalent nature of this integrated spin/charge doping results in severely limited chemical solubility in (Ga,Mn) As, restricting specimen fabrication to metastable thin films by molecular beam epitaxy; second, the simultaneous spin and charge doping precludes the possibility of individually tuning the spin and charge degree of freedom. A new type of ferromagnetic DMS based on I-Ⅱ-V group can overcome both of these challenges. Li(Zn,Mn) As utilizes excess Li concentration to introduce hole carriers, while independently making the isovalent substitution of Mn2+ for Zn2+ in order to achieve local spin doping. With no heterovalent substitution to restrict chemical solubility, bulk samples of Li(Zn,Mn) As are successfully fabricated. However, one drawback of Li(Zn,Mn) As is its use of the toxic element As. The isostructural direct-gap semiconductor LiZnP also undergoes a ferromagnetic transition upon Mn doping, and its bulk magnetic properties are very similar to those of LiZnAs. In this paper, the geometric structure of pure LiZnP, Ag doped, Cr doped, and Ag-Cr co-doped LiZnP new diluted magnetic semiconductor are optimized by using the first-principles plane wave ultra-soft pseudo-potential technology based on the density function theory. Then we calculate the electronic structure, magnetism, formation energy, differential charge density, and optical properties of the doped systems. The results show that the material is a paramagnetic metal after single doping of the nonmagnetic element Ag. When magnetic element Cr is doped with LiZnP, sp-d orbital hybridization makes the peak of density of state nearly EF-split, leading the system to become metallic ferromagnetism. However, Ag-Cr co-doped LiZnP changes into half-metallic ferromagnetism, which is completely different from the single doping system. The band gap decreases slightly, and the electrical conductivity is enhanced. Meanwhile, the formation energy of the system becomes lower, the bond between atoms strengthens, and the stability of the unit cell becomes stronger. A comparison of the optical properties indicate that the imaginary part of dielectric function and the optical absorption spectrum both present new peaks in low energy region in the doped systems. Ag-Cr co-doped LiZnP has the highest dielectric peak. Meanwhile, the complex refractive index function changes obviously in a low energy region, and the absorption edge extends to the low energy direction. The system enhances the absorption of low-frequency electromagnetic waves.