Wettability alteration as the main mechanism of improved oil recovery in carbonates during low salinity/engineered water flooding (LS/EWF) is a complex phenomenon due to high heterogeneity of rock. During LS/EWF, wettability changes when electrochemical interactions at carbonate-brine interface happen. Anhydrite impurity in carbonates is one of the most important parameters affecting the electrochemical interactions at the rock-brine interface and the wettability alteration process. Therefore, the success of LS/EWF in carbonate reservoirs lies in perceiving the role of impurities such as anhydrite, from a geochemical and dissolution point of view.Modified flotation tests (MFT) were performed on two rock samples (calcite and a mixture of calcite and 10 wt% of anhydrite) to assess the wettability alteration which showed a non-monotonic wettability effect as the presence of anhydrite lowered the optimum salinity from 10-times diluted seawater (SW/10) to SW/25. Mineral dissolution and zeta potential measurement showed no comprehensive correlation with the wettability state of particles obtained from MFTs. To resolve this challenge, a diffuse double layer (DDL) based surface complexation model (SCM) was developed using PHREEQC geochemical package to shed light on the anhydrite role during the desorption of oil acidic components from the rock surface imposed on various brines. The model was validated using measured zeta potential. The DDL-based SCM proposed an anhydrite dominant window in which the presence of anhydrite, its dissolution, and in-situ supply of SO42-, lead to altering the wettability to more water wetness.This work is significant to explain the effect of anhydrite impurity on the performance of low salinity water injection using experimental data and DDL-based SCM, while the simple techniques of rock dissolution and zeta potential are not able to justify the non-monotonic behavior of wettability of the carbonates. Also, it introduces a new quantitative parameter of the wettability state of carbonate surface by considering the adsorbed carboxylic acid components on the calcite surface reported by SCM.