A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence model are proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Prediction gives the bubble and liquid velocities, bubble volume fraction, bubble and liquid Reynolds stresses and bubble-liquid velocity correlation. For predicted two-phase velocities and bubble volume fraction there is only slight difference between these two models, and the simulation results using both two models are in good agreement with the particle image velocimetry (PIV) measurements. Although the predicted two-phase Reynolds stresses using the FSM are in somewhat better agreement with the PIV measurements than those predicted using the ASM, the Reynolds stresses predicted using both two models are in general agreement with the experiments. Therefore, it is suggested to use the ASM two-phase turbulence model in engineering application for saving the computation time.