This paper is devoted to the partial regularity of suitable weak solutions to the system of the incompressible shear-thinning flow in a bounded domain Ω (C) Rn,n ≥ 2.It is proved that there exists a suitable weak solution of the shear-thinning fluid in the n-D smooth bounded domain (for n ≥ 2).For 3D model,it is proved that the singular points are concentrated on a closed set whose 1 dimensional Hausdorff measure is zero.