Abstract: Analytical investigation of liquid Reynolds stress in shear bubbly flow with intermediate Reynolds numbers is absent.In this paper, the velocity field around a sphere bubble in linear shear liquid is assumed to be the linear superposition of the velocity field of uniform liquid passing a sphere bubble and the linear shear velocity field.The formula of shear liquid Reynolds stress was derived by averaging the velocity field in the cell-ensemble averaging method, and the formula was corrected under conditions of intermediate Reynolds number.The formula was compared with that of Sato, and the predicted results of local liquid velocity of the fully developed upward bubbly flow in pipes were compared with the experimental data.The results show that the formula is valid and accurate in prediction.