Electrochemical interactions at calcite-water interface are characterized by the zeta potential and play an important role in many subsurface applications. In this work we report a new physically meaningful surface complexation model that is proven to be efficient in predicting calcite-water zeta potentials for a wide range of experimental conditions. Our model uses a two-stage optimization for matching experimental observations. First, equilibrium constants are optimized, and the Stern layer capacitance is optimized in the second stage. The model is applied to a variety of experimental sets that correspond to intact natural limestones saturated with equilibrated solutions of low-to-high salinity, and crushed Iceland Spar sample saturated with NaCl at non-equilibrium conditions. The proposed linear correlation of the Stern layer capacitance with the ionic strength is the main novel contribution to our surface complexation model without which high salinity experiments cannot be modelled. Our model is fully predictive given accurately known conditions. Therefore, the reported parameters and modelling protocol are of significant importance for improving our understanding of the complex calcite-water interfacial interactions. The findings provide a robust tool to predict electrochemical properties of calcite-water interfaces, which are essential for many subsurface applications including hydrology, geothermal resources, CO2 sequestration and hydrocarbon recovery.