Viscosified acids are desired in several oilfield applications such as in acid diversion and acid fracturing operations. The study aimed to delineate the rheological properties of a novel amine type surfactant and viscosified acid-surfactant solutions. The steady shear and dynamic rheological properties were evaluated by varying the surfactant, acid, and salt concentration. Such a study is required to gauge the suitability of the viscosifying agent in acid stimulation jobs. The surfactant solutions without acid showed shear-thinning behavior, whereas those with acid showed a Newtonian plateau over a wide shear rate range before undergoing shear thinning. This means that over a wide shear rate range, the acid-surfactant solutions become independent of applied shear. At low shear rates, the viscosity of the surfactant was higher compared with the surfactant-acid solution. However, at high shear rates, the viscosity of the surfactant was lower compared with the viscosity of the surfactant-acid solution. There was an optimal salt concentration that improved the viscosity and elasticity of the acid-surfactant solutions. Thus, the rheology of the surfactant solution can be improved by adding both acid and salt. The elastic properties of acid-surfactant solutions were also better compared with the elastic properties of pure surfactant. The addition of acid improved the elastic properties of the surfactant solutions. Constant viscosity over a range of shear rate is a suitable application for acid fracturing operations in which the acid leak-off will be minimal due to the high viscosity. Also, brines in most of the carbonate formation consist of high loading of calcium chloride which was found to have a positive effect on the viscosity. Increasing the calcium chloride leads to an increase in viscosity, and then subsequently decreases the viscosity. This shows that the acid and salt concentration plays a role in modifying the rheological properties of the surfactant solutions.