The evolution properties of geometric quantum discord (GQD) of the Heisenberg XXZ spin model in a non-Markovian environment are studied using the quantum state diffusion method. The influences of environmental correlation parameters γ, coupling constants in the xy plane Jxy, coupling constants in the z direction Jz, applied magnetic field B and Dzyaloshinskii-Moriya (DM) interactions on the GQD dynamics are analyzed. The results show that the shorter the γ is, the more obvious the non-Markovian characteristics of the environment are, the better it is to effectively improve the GQD; Jxy and Jz have different effects on the GQD when different initial states are selected; in the non-Markovian environment, increasing the magnetic field B can improve the GQD, while the DM interaction will lead to decaying oscillations of the GQD. It is worth mentioning that the GQD can be effectively induced from the entanglement-free initial state system.