Low-salinity brine injection has emerged as a promising, cost-effective improved oil recovery (IOR) method for waterflooding reservoirs. Laboratory tests and field applications show that low-salinity waterflooding could lead to significant reduction of residual oil saturation. There has been a growing interest with an increasing number of low-salinity waterflooding studies. However, there are few quantitative studies on flow and transport behavior of low-salinity IOR processes. This paper presents a general mathematic model (1) to incorporate known IOR mechanisms and (2) to quantify low-salinity waterflooding processes. In our mathematical conceptual model, salt is treated as an additional "component" to the aqueous phase, based on the following physical considerations: salt is transported only within the aqueous phase by advection and diffusion, and also subject to adsorption onto rock solids; relative permeability, capillary pressure, and residual oil saturation depend on salinity. Interaction of salt between mobile and immobile water zones is handled rigorously using a multi-domain approach. Fractured rock is handled using the multiple-continuum model or a discrete-fracture modeling approach. The conceptual model is implemented into a general-purpose reservoir simulator for modeling low-salinity IOR processes, using unstructured, regular, and irregular grids, applicable to 1-D, 2-D, and 3-D simulation of low-salinity water injection into porous media and fractured reservoirs. As demonstrated, the model provides a general capability for quantitative evaluation of low-salinity waterflooding in site-specific investigations.