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It is shown in this paper that suitable weak solutions to the 6D steady incompressible Navier-Stokes are Hölder continuous at 0 provided that ∫ B 1 | u (x) | 3 d x + ∫ B 1 | f (x) | q d x or ∫ B 1 | ∇ u (x) | 2 d x + ∫ B 1 | ∇ u (x) | 2 d x (∫ B 1 | u (x) | d x) 2 + ∫ B 1 | f (x) | q d x with q > 3 is sufficiently small, which implies that the 2D Hausdorff measure of the set of singular points is zero. For the boundary case, we also obtain that 0 is regular provided that ∫ B 1 + | u (x) | 3 d x + ∫ B 1 + | f (x) | 3 d x or ∫ B 1 + | ∇ u (x) | 2 d x + ∫ B 1 + | f (x) | 3 d x is sufficiently small. These results improve previous regularity theorems by Dong-Strain ([8] , Indiana Univ. Math. J., 2012), Dong-Gu ([7] , J. Funct. Anal., 2014), and Liu-Wang ([27] , J. Differential Equations, 2018), where either the smallness of the pressure or the smallness of the scaling invariant quantities on all balls is necessary. [ABSTRACT FROM AUTHOR]