The often-disturbing adverse effects of inflation in developing economies such as Nigeria necessitates developing dynamic inflation forecasting models for appraising shocks on macroeconomic variables. This work utilizes the Box-Jenkins methodology to develop Seasonal Autoregressive Integrated Moving Average (SARIMA) model to predict peak time inflation in Nigeria’s inflation time series from January 2001 to December 2015 obtained from National Bureau of Statistics, Abuja. A test of parameter estimates was performed on the suggested models and, using the AIC and BIC criteria, SARIMA(1,1,2)(2,0,1)12 model was identified as the most fitted model. The diagnostic test of the residuals using ACF and PACF of residual plots showed that they follow white noise process. The result of the monthly forecast indicated that Nigeria will experience high (double digit) inflation rates which will be at its peak in the months of August and September and its lowest rate occurs in January of the year. The information contained here can be useful to ensure monetary and fiscal policies that will stabilize the economy.