To compare the fitting effect of ARIMA model and grey model (GM) (1,1) in the under five mortality rate(U5MR) in Shenzhen, and to predict the U5MR in Shenzhen in the next 3 years, so as to provide scientific basis for the formulation of child health care plan.

Taking the U5MR in Shenzhen from 2005 to 2022 as the original data, ARIMA model and GM (1,1) model were constructed to fit the child mortality rate. The mean absolute error (MAE) and mean absolute percentage error (MAPE) were used to compare the fitting effect of the two models.

From 2005 to 2022, the U5MR in Shenzhen showed a downward trend, lower than the national average. The MAE of the constructed ARIMA model and GM (1,1) model was 0.30 and 0.24, respectively, and the MAPE was 11.53% and 8.73%, respectively. The fitting effect of the GM (1,1)model was good. The U5MR in Shenzhen from 2023 to 2025 would be 1.27 ‰, 1.18 ‰, and 1.09 ‰, respectively, predicted by GM (1,1) model.

The fitting effect of GM (1, 1) model on U5MR in Shenzhen is better than that of ARIMA model, and it is predicted that the U5MR in Shenzhen will decrease year by year in the next 3 years.