The Middle East marine carbonate reservoirs are the primary targets for global crude oil exploration and production. In contrast to the clastic rock reservoirs, the marine carbonate reservoirs have undergone more complicated deposition, diagenesis and transformation, and the rock surface tends to be oil-wet or mixed-wet. One of the most effective methods for enhancing oil recovery in marine carbonate reservoirs is the use of an ion matched (IM)-surfactant (S) system to alter the wettability of rock surfaces. In this paper, we propose a microscale mathematical model of wettability alteration-coupled fluid flow by considering oil–water two-phase flow, wettability alteration, solute advection- diffusion and surfactant adsorption. The proposed microscale mathematical model is solved using the multi-component lattice Boltzmann model, and its accuracy is further verified. Finally, the effects of displacing fluid, ion-matched water concentration and surfactant concentration on oil mobilization at pore-scale are studied. Results show that, ion-matched water has a positive effect on wettability alteration, and typically shifts the cross-point of oil–water relative permeability curve to the right. The concentration of ion-matched water primarily affects fluid morphology of the wetting-phase and has little effect on phase permeability. After adding surfactant to the ion-matched water, the Euler coefficient of oil-phase gradually increases as the displacement continues, a large amount of remaining oil is gradually dispersed into scattered oil droplets and the oil-phase relative permeability is further improved.