Among other mathematical difficulties, the variational inequality problem is a broad problem that includes nonlinear equations, optimization problems, complementarity problems, and fixed-point problems. The pricing model of the option, economic equilibrium issues, and specific kinds of partial deferential equations are all studied using variational inequality. In particular classical-variational inequality problem has been broaden to survey a large group of problems arising in optimization theory, physics, economics, financial, structural transportation, and so forth. The study has expanded and epitomized in various fields through different techniques and ideas. Variational Inequality Problem has already defined in various infinite dimensional spaces like manifolds, Housdorff topological vector spaces, Hilbert spaces, Banach space, H-space etc. Also some authors has already introduced vector F-variational inequality problems in ordered topological vector spaces and differentiable ?-manifolds. Also, in one of our previous work we have already defined variational inequality problem on Cesàro sequence space and proved some result like monotonicity and existence theorem on it. The main aim of the work is to introduce the generalized version of variational inequality problems in non-absolute Cesàro sequence spaces Here at first,we have defined generalized variational inequality problem (GVIP) and generalized dual variational inequality problem(GDVIP) on non absolute Cesàro sequence space. We have defined homotopy and functional homotopy for our need.Next we have used KKM mapping to prove existence theorem of generalized Variational inequality problem on a non-absolute Cesàro sequence space to its dual space. Also we have proved some more properties like monotonicity of GVIP on ?- dual of non absolute Cesàro sequence space.