In this paper, we propose a parametric accelerated failure time (AFT) hazard-based regression model with the extended alpha-power exponential (EAPE) baseline distribution. The proposed model is called the extended alpha-power exponential-AFT (EAPE-AFT) regression model. We show that the EAPE distribution is closed under the AFT model. The parameters of the proposed EAPE-AFT model have been estimated by using the method of maximum likelihood estimation. An extensive simulation study was also conducted to examine the performance of the estimates under several scenarios based on the shapes of the baseline hazard function. Finally, real-life censored survival data has been used to illustrate the applicability of the proposed model.