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In this paper, we introduce a new problem, the modified split generalized equilibrium problem, which extends the generalized equilibrium problem, the split equilibrium problem and the split variational inequality problem. We introduce a new method of an iterative scheme { x n } for finding a common element of the set of solutions of variational inequality problems and the set of common fixed points of a finite family of quasi-nonexpansive mappings and the set of solutions of the modified split generalized equilibrium problem without assuming a demicloseness condition and T ω : = ( 1 - ω ) I + ω T , where T is a quasi-nonexpansive mapping and ω ∈ ( 0 , 1 2 ) ; a difficult proof in the framework of Hilbert space. In addition, we give a numerical example to support our main result., Competing Interests: The authors declare that they have no competing interests.