Low salinity flooding has been proposed as a promising method for enhanced oil recovery, but the underlying mechanism remains unclear especially for carbonate reservoirs. This work investigates the effect of water salinity in altering the wettability of nano-slit pores for three types of calcite surfaces (i.e., a neutral nonpolar {1 0 (1) over bar 4} surface, and the polar {0 0 0 1} surface with positively and negatively charged surfaces) using classical, equilibrium molecular dynamic (EMD) simulations. In addition, non-equilibrium MD simulations (NEMD) reveal the influence of wettability on the oil transport properties in a nano-pore at different salt concentrations of sodium chloride (NaCl) (0.20 M, 0.50 M, and 1.00 M). Results show that increasing water salinity has little effect on the wettability of a nano-pore comprised of neutral calcite surfaces. For a calcite nano-slit pore comprised of charged surfaces, however, the dipole-ion interaction alters the surface wettability creating a more hydrophilic surface due to the hydration effect of ions at elevated salt concentrations. While a partially decane-wet neutral nonpolar calcite surface greatly inhibits the movement of an oil droplet in the pore, greater oil mobility is achieved for dipolar nano-pores, especially at elevated salt concentrations.