Amphiphilic-polymer flooding, which can increase water viscosity, decrease oil viscosity, and improve oil displacement efficiency, is a promising oil exploitation method for heavy oil. Due to oil–water emulsification, shear-thinning, and changes in oil viscosity when determining the relative permeability data of new amphiphilic polymers, the conventional J.B.N. method is not accurate. This paper presents a new method called the iso-permeability point trial method to determine the relative permeability curve by combining the J.B.N. method, the Corey model, and the relationship between water saturation and the relative permeability ratio. To avoid using polymer viscosity, a mathematical equation was derived based on the characteristics of the relative permeability curve. The results indicate that the new method is feasible and the obtained curve is more reasonable and smooth. The influence of concentration, permeability, and oil viscosity on amphiphilic-polymer displacement relative permeability was also analyzed, demonstrating that under the same water saturation, the water relative permeability is lower than that of water flooding but the oil relative permeability is bigger, which manifests as the iso-permeability point moves to the right and results in a lower residual oil saturation. In addition, the aforementioned trends are more obvious when the amphiphilic-polymer concentration is high, formation permeability is low, and oil viscosity is low.