Permeability of hydrate-bearing sediments is the key parameter to determine the gas production performance, which is mainly affected by the pore morphology and hydrate saturation. Existing models of permeability could not well capture the dynamic characteristic of permeability in sediments with changing hydrate saturation and pore morphology. In this paper, a novel normalized permeability model using logistic function linked different hydrate pore morphology evolution was established by modifying tortuosity, surface area and pore shape factor simultaneously in Kozeny-Carman equation. It was verified by different published data and compared with other models. The introduced critical hydrate saturation and transitional intensity of hydrate pore morphology were optimized by genetic algorithm. Results indicated that this model was more powerful than existed models and better captured the permeability evolution in hydrate-bearing sediments at various conditions. The critical hydrate saturation and transitional intensity of hydrate pore morphology dominated the characteristics of permeability evolution. In addition, the effect of porosity would not be ignored especially below the critical hydrate saturation when hydrate pore morphology changed from pore filling to grain coating. The proposed model brings reliable predictions and mechanistic understandings of the permeability evolution in hydrate-bearing sediments, and builds fundamental theory for development of natural gas hydrate in safety and efficiency.