Many conventional reservoirs use water flooding to displace oil and supply energy to the formation. However, previous studies have established that water injection influences the pore structure of the reservoir rock, and thus, many important physical properties change with time during development. Most reservoir simulators neglect the alteration of reservoir properties during simulation, and thus, fail to reflect the real dynamic of the fluid flow and production performance. In this paper, a new parameter known as surface flux is introduced to continuously characterize the time-variation of a property during simulation. This new method overcomes the disadvantage of the previous characterization approach, which is strongly dependent on grid size. A new numerical simulation software in which reservoir properties are considered functions of surface flux is developed based on the black oil model, and the new simulator is validated against commercial software. Additionally, the proposed method is validated in overcoming the disadvantage of the latest approach, which is dependent on grid size. Furthermore, the time-variation effects of different parameters are investigated, and the ultimate oil recovery of the synthetic reservoir is found to increase when taking the time-variation of the relative permeability curve into account, whereas the ultimate recovery of the synthetic reservoir declines when the time-variation of the absolute permeability is incorporated. Eventually, the newly developed simulator is applied to a real water flooding reservoir to illustrate how this simulator can facilitate the history matching process and enhance the numerical model reliability. The field water cut predicted with the traditional black oil simulator after history matching is higher than that of the real production, which is because the time-variation mechanism is neglected. The water cut obtained by our simulator after history matching can readily match the actual data because it successfully represents the variation in the reservoir properties during production.