Traditionally, the gas-lift pump has been used to lift corrosive or toxic liquid due to its simple structure and maintenance. It is also considered as a technically feasible system for the development of deep-ocean minerals and as a means to sequestrate $CO_2$ gas into the ocean. Donor-cell scheme or Forward-Time and Backward- Space (FTBS), which is commonly used in solving advection equation such an air-lift system, is very stable but causes numerical diffusion. In order to reduce numerical diffusion or dissipation by the first-order upwind scheme, CIP (Cubic-Interpolated Propagation/Constrained Interpolation Profile) has been applied to bubble and slug flows in a gas-lift pumping system. The GLAD (Gas-Lift Advanced Dissolution) model using CIP method were validated by comparison with gas-liquid two-phase experiments and the effectiveness of the CIP method over the typical one has been demonstrated from the simulation of gas-liquid two-phase slug flow.