This work presents a numerical investigation on steady internal, external and surface flows of a liquid sphere immersed in a simple shear flow at low and intermediate Reynolds numbers. The control volume formulation is adopted to solve the governing equations of two-phase flow in a 3-D spherical coordinate system. Numerical results show that the streamlines for Re = 0 are closed Jeffery orbits on the surface of the liquid sphere, and also closed curves outside and inside the liquid sphere. However, the streamlines have intricate and non-closed structures for Re not equal 0. The flow structure is dependent on the values of Reynolds number and interior-to-exterior viscosity ratio. (C) 2014 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.