Infant Mortality Rates (IMR) are important indicators of health status of any country. This research presents Time Series Analysis using Exponential Smoothing and Moving Averages (MA). Six years data on infant mortality covering 2016 to 2021 was obtained from Yobe State Specialist Hospital Damaturu. We used Single Exponential Smoothing, which at =2, the model showed a smoothed trend of infant mortality over the period of 72 months. A forecast made based on this smoothed trend indicated a constant rate of infant mortality over the period of 8 months with MAPE = 17.9165, MAD = 4.5133 and MSD = 30.2982. We also studied nature of trend using Moving Averages (MA) and forecast made at length = 4 showed a constant rate of forecast over the period of 8 months with MAPE = 19.3504, MAD = 4.8377, and MSD = 34.1556. Based on the three accuracy measures, single exponential smoothing method presented a better fit to the data. Highest infant mortality was observed in 2021 with total death of 331 which represents 17.08% of the total deaths.