The use of salt rock for underground radioactive waste disposal facilities requires a comprehensive analysis of the creep-damage process in salt rock. A computer-controlled creep setup was employed to carry out a creep test of salt rock that lasted as long as 359 days under a constant uniaxial stress. The acoustic emission (AE) space-time evolution and energy-releasing characteristics during the creep test were studied in the meantime. A new creep-damage model is proposed on the basis of a fractional derivative by combining the AE statistical regularity. It indicates that the AE data in the non-decay creep process of salt rock can be divided into three stages. Furthermore, the authors propose a new creep-damage model of salt rock based on a fractional derivative. The parameters in the model were determined by the Quasi-Newton method. The fitting analysis suggests that the new creep-damage model provides a precise description of full creep regions in salt rock.