A numerical method based on finite volume method for solving Fokker-Planck equation on a unit sphere was first developed to simulate numerically the fiber orientation distribution of fiber suspensions flowing through a curved expansion duct. The momentum equation with fiber extra stress was used to explore the rheological properties of the fiber suspensions. The second-order fiber orientation tensors in present simulation are compared with the previous numerical results for validating the model and computational code. The results showed that the pressure increases from inlet to outlet, and changes along the lateral direction nonmonotonically except at outlet. The extra shear stress and normal stress difference decrease from inlet to outlet, and changes along the lateral direction nonmonotonically. The effect of fiber aspect ratio on the extra shear stress and normal stress difference is negligible near the wall region. The extra shear stress and normal stress difference increase with the fiber aspect ratio near the centerline. The lateral distribution curves of extra shear stress and normal stress difference become flat with increasing the distance from the inlet. POLYM. ENG. SCI., 50:1994-2003, 2010. (C) 2010 Society of Plastics Engineers