Abstract: At present, China's aging population is becoming increasingly prominent. Accurately predicting the number and density distribution of the elderly population in the future is conducive to accelerating the development of aged care services and has important reference value for formulating relevant policies and social development. In this paper, a novel SM-FGM model is constructed to predict the quantity and density distribution of the elderly population in Nanjing from 2021 to 2030. The combined model combines the advantages of fractional-order accumulation and self-memory algorithm and has good prediction accuracy and generalization ability. Fractional-order accumulation can effectively weaken the randomness of the original data sequence, and the memory function in the self-memory algorithm breaks through the limitation that the traditional grey model is sensitive to the initial value. The results show that the number of elderly people in Nanjing's administrative districts will show a high base and high growth trend in the next 10 years. There are significant differences in the density of elderly people among the administrative districts. The density of elderly people in the central city is higher and becomes a dense area for the elderly, and the population density gradually decreases with the direction of suburban areas.