This study uses annual time series data on under five mortality rate (U5MR) for Bulgaria from 1960 to 2020 to predict future trends of U5MR over the period 2021 to 2030. Residuals and forecast evaluation statistics indicate that the applied Holt’s linear model is stable in forecasting future trends of under-five mortality rate in Bulgaria. Optimal values for smoothing constants α and β are 0.8 and 0.1 respectively based on minimum MSE. The double exponential smoothing model projections showed that annual U5MR will continue to decline over the out of sample period. Therefore authorities in Bulgaria are encouraged to draft child health policies that will keep under five mortality under control.