Wettability alteration would play a significant role in the hydrocarbon displacement as it can improve oil recovery factor both in conventional and unconventional reservoirs. Therefore, accurate prediction of this parameter would be of importance in displacement sweep efficiencies. In this paper, we aimed to experimentally investigate wettability changes in the presence of a nonionic natural surfactant (Cedar) for different carbonate mineral samples. To do this, Imbibition and USBM tests were taken into consideration to predict capillary pressure and how it affects oil production rate. It is observed that the presence of Cedar had a profound impact on the wettability and capillary pressure for calcite and dolomite samples. Due to the different composition of rock minerals, Cedar has a good effect on both core sample (calcite and dolomite), whereas the oil recovery for dolomite cores is more than calcite cores. This change for calcite cores corresponding oil-wet to neutral-wet or slightly water-wet and for dolomite samples become to water-wet. In addition, the most Sor decreasing occurs in dolomite samples particularly in D1 (14%). Moreover, the oil recovery for reservoir samples is less than mineral samples.