In　this　paper,　we　study　the　global　regularity　to　a　three-dimensional　logarithmic　sub-dissipative　Navier-Stokes　model.　This　system　takes　the　form　of　partial　derivative(t)u　+　(D(-1/2)u)　.　del　u　+　del　p　=　-A(2)u,　where　D　and　A　are　Fourier　multipliers　defined　by　D　=　vertical　bar　del　vertical　bar　and　A　=　vertical　bar　del　vertical　bar　ln(-1/4)(e　+　lambda　ln(e　+　vertical　bar　del　vertical　bar))　with　lambda　＞=　0.　The　symbols　of　the　D　and　A　are　m(xi)　=　vertical　bar　xi　vertical　bar　and　h(xi)　=　vertical　bar　xi　vertical　bar/g(xi)　respectively,　where　g(xi)　=　ln(1/4)　(e　+　lambda　ln(e　+　vertical　bar　xi　vertical　bar　lambda　＞=　0.　It　is　clear　that　for　the　Navier-Stokes　equations,　global　regularity　is　true　under　the　assumption　that　h(xi)　=　vertical　bar　xi　vertical　bar(alpha)　for　alpha　＞=　5/4.　Here　by　changing　the　advection　term　we　greatly　weaken　the　dissipation　to　h(xi)　=　vertical　bar　xi　vertical　bar/g(xi).　We　prove　the　global　well-posedness　for　any　smooth　initial　data　in　H-s(R-3),　s　＞=　3　by　using　the　energy　method.