Abstract: The concept of generalized Levitin-Polyak well-posedness for symmetric generalized strong vector quasi-equilibrium problem and properly quasi-convexity for set-valued mappings are introduced.By means of Kakutani-Fan-Glicksberg’s fixed point theorem, the existence of solutions to this problem is obtained.Meanwhile, the proof of symmetric generalized strong vector quasi-equilibrium problem is generalized Levitin-Polyak wellposedness is done.Finally, the examples to show the conditions required by the main theorem are easily found are given.