This study examined the dynamics of inflationary process in Nigeria over the period 1981 - 2015, using the bounds testing approach to cointegration. Empirical results indicated that inflation in Nigeria proxied by CPI exhibited a strong degree of inertia. The econometric results showed that past inflation and average rainfall appeared to have been the main determinants of inflationary process in Nigeria over the study period. We also found strong evidence of the importance of money supply in the inflation process, lending credence to the dominance of the monetarist proposition on inflation dynamics in Nigeria. Thus, the paper recommended among others, the continuous moderation of growth in money supply by the central bank and adopting consumers' expectations of inflation as an input into the monetary policy process.