Salt precipitation occurring in fault zone, due to CO2-brine co-leakage, would create an opportunity to prevent CO2 leakage along fault, i.e., salt-precipitation-based self-remediation model. To investigate the new model, the physical model on salt precipitation was proposed, considering co-leakage of CO2 and brine along fault. Theoretical model was given on salt precipitation, and the numerical model was established to validate the salt precipitation occurring in fault zone. The numerical results indicated that salt precipitation indeed occurred in fault zone, and CO2 leakage rate was obviously decreased after salt precipitation. Importantly, evolution of salt precipitation in fault was concluded, from viewpoint of co-leakage of CO2 and brine along fault, and degree of salt precipitation was characterized, using representative parameters such as the starting time, ending time, lasting time of salt precipitation, and solid saturation. Especially, the self-remediation model for CO2 leakage based on salt precipitation was confirmed feasibly. The self-remediation capacity was closely related to degree of salt precipitation (or lasting time of salt precipitation), and was directly evaluated by the decreasing in CO2 leakage rate before and after salt precipitation. Finally, the parametric analyses showed that: (1) the potential correlation was found among the lasting time of salt precipitation, solid saturation and self-remediation capacity; (2) the higher CO2 injection rate and fault permeability, the smaller fault width and permeability of lower saline aquifer were helpful for salt precipitation and self-remediation capacity; (3) no salt precipitation occurred for the smaller CO2 injection rate and fault permeability, the larger fault width and permeability of lower saline aquifer.