This paper studies the thermodynamic properties of Gauss-Bonnet black holes in de Sitter (dS) space. When the Gauss-Bonnet coefficient is positive, a locally stable small black hole appears in 5 dimensions, but disappears in higher dimensions (d ≥ 6), where the black hole is always thermodynamically unstable. The cosmological horizon is always locally stable, regardless of the spacetime dimension. However, the pure dS space is globally preferred. When the Gauss-Bonnet coefficient is negative, there is a constraint on its value, beyond which the gravity theory is not well-defined. This leads to an upper bound on the black hole horizon radius where it coincides with the cosmological horizon, and a lower bound depending on the coefficient and spacetime dimension. Within the physical phase space, the black hole horizon is always thermodynamically unstable, while the cosmological horizon is always stable. The pure dS space remains globally preferred. These results are consistent with the argument that the pure dS space corresponds to an ultraviolet (UV) fixed point of the dual field theory in the dS/CFT correspondence. The thermodynamic stability of the black hole and cosmological horizons is analyzed, showing that the black hole horizon has a positive heat capacity in some cases, while the cosmological horizon is always stable. The paper also discusses the phase structure and thermodynamic properties of these horizons, showing that the pure dS space is globally preferred due to lower free energy. The results highlight the importance of the Gauss-Bonnet term in determining the thermodynamic stability and phase structure of black holes in dS space.This paper studies the thermodynamic properties of Gauss-Bonnet black holes in de Sitter (dS) space. When the Gauss-Bonnet coefficient is positive, a locally stable small black hole appears in 5 dimensions, but disappears in higher dimensions (d ≥ 6), where the black hole is always thermodynamically unstable. The cosmological horizon is always locally stable, regardless of the spacetime dimension. However, the pure dS space is globally preferred. When the Gauss-Bonnet coefficient is negative, there is a constraint on its value, beyond which the gravity theory is not well-defined. This leads to an upper bound on the black hole horizon radius where it coincides with the cosmological horizon, and a lower bound depending on the coefficient and spacetime dimension. Within the physical phase space, the black hole horizon is always thermodynamically unstable, while the cosmological horizon is always stable. The pure dS space remains globally preferred. These results are consistent with the argument that the pure dS space corresponds to an ultraviolet (UV) fixed point of the dual field theory in the dS/CFT correspondence. The thermodynamic stability of the black hole and cosmological horizons is analyzed, showing that the black hole horizon has a positive heat capacity in some cases, while the cosmological horizon is always stable. The paper also discusses the phase structure and thermodynamic properties of these horizons, showing that the pure dS space is globally preferred due to lower free energy. The results highlight the importance of the Gauss-Bonnet term in determining the thermodynamic stability and phase structure of black holes in dS space.