In this paper we obtain the spacetime of a cosmic string with inner structure of r₀ radius, using modified gravity of Gauss-Bonnet (GB). The Gauss-Bonnet gravity modifies the Einstein-Hilbert scalar incorporating higher-order terms on action. We analyzed the string’s space-time inside  and outside of her core, inside r < r₀, we will assume that the energy distribution  of the cosmic  string  is constant,  σ = σ₀, and outside  null,  σ = 0, for both  we determined  the solution  by using  a specific form of the Gauss-Bonnet scalar, f (G)= α Gⁿ α being a constant and  n an integer.