Abstract: The global regularity of the supercritical hyper-dissipative three-dimensional Navier-Stokes equation in the whole space was studied. This model modified the dissipation term in the classical Navier-Stokes equation, and the dissipative term Δu here is replaced by －D^2u, where D is a Fourier multiplier. The global regularity of the critical and supercritical high dissipative case of Navier-Stokes equation was proved when the symbol is m(ξ)=|ξ|α,α≥5/4. This slightly by establishing global regularity under the condition that m(ξ)=|ξ|α/g(|ξ|) for all sufficiently large ξ and some nondecreasing function g:R+→R+such that∫??1ds/(sg(s)4)=+??   were improved. By the classical energy method, the global regularity of the model was proved in a slightly weaker condition.