In this study, pure and self-healing asphalt mixture samples were obtained by adding capsules containing waste vegetable oil to mixtures at 0.25, 0.50, 0.75 and 1.00% ratios. Afterwards, creep test with a constant stress was carried out on the samples, and the resistance of asphalt mixtures against permanent deformation was investigated. Relaxation modulus values were obtained by using the creep compliance values that measured at the end of the experiment with mathematical transformations. Then, the relaxation modulus results were fitted to the Generalized Maxwell Model, which is a common model used to represent the viscoelastic properties of asphalt mixtures, and Prony series parameters were obtained. The results showed that the addition of capsule reduced the permanent deformation strength of the asphalt mixture. In addition, the curve fitting processes were successfully performed and the desired parameters were obtained with high accuracy.