Achieving high economic growth rate while maintaining low inflation rate, has become the main objective of monetary authorities all over the world. Indeed, empirical literature reflects that high inflation rates are detrimental to long run growth and entail welfare costs. To achieve this objective, central banks have availed different options from time to time which include inflation targeting. Monetary authorities in Tanzania have been targeting an inflation level of around 5 percent per annum for economic policy purposes. However, when high inflation is to be controlled, tight monetary policy is put in place which might in turn affect the economic activity. Also, the Tobin effect suggests that inflation causes individuals to substitute out of money and into interest earning assets, which leads to greater capital intensity which in turn promotes economic growth. Against these major points, this paper examines a non linear relationship between inflation and economic growth using both a quadratic and threshold endogenous models and attempts to identify the existence of threshold effects between these variables. The paper uses a data set spanning from 1967 to 2015. The most interesting finding of the estimations is that the estimated coefficient of the linear term of inflation is negative while the estimated coefficient of the square term of inflation is positive, suggesting a U-shaped effect as opposed to inverse or inverted U-shaped relationship found in other countries by previous studies. These results suggest that the Tobin effect may be valid for high inflation, in which people strongly realize the importance of substituting money for interest-bearing assets. This leads to an increase in capital investment, and in turn, an increase in economic growth even with high inflation rate. However, this U-shaped relationship between inflation and economic growth suggests that, the economy is better off at extremely low inflation episodes. The optimal inflation rate that ranges between 3.25 percent and 3.75 percent is obtained by minimizing the residual sum of squares and/or maximizing adjusted R-squared. These findings have some policy implications for the policymakers and development partners. The paper is consistent with policy suggestions by international agencies. Efforts to minimize inflation to a very low level are likely to have a positive effect on economic growth.