The exact subgradient algorithm for solving the equilibrium problem (EP(f,Fix(T))) of sets over the fixed point of non-expansive operator causes computational complexity and poor convergence.To overcome the defect,an inexact subgradient algorithm for the EP(f,Fix(T)) was presented.A convex set assured by given parameter was selected,the intermediate iterative point was constructed by using the non-accurate subgradient projection algorithm and the image,under firmly non-expansive operator of the linear combination of the current iterative point and middle iterative point was taken as the next iteration point.Under suitable conditions,the global convergence of the algorithm was verified.