The price of money is "the goods and services" it can buy, which means, if money is plenteous will chase fewer or less amount of goods and services than it could actually do. Under normal conditions, money-inflation relationship is not instantaneous and so we should not expect all outcomes of currently implemented monetary policy actions to happen in the same current period. What is not clearly known for Tanzania is the time it takes a change in money supply to start impacting on inflation. The main objective of this paper is therefore to determine this time lag. Seasonally adjusted monthly data for the period 1994-2006 are used in the analysis and a GARCH model is applied in investigating inflation-money relationship. Estimation results indicate that a current change in money supply would affect inflation rate significantly in the seventh month ahead. They show further that the impact of money supply on inflation is not a sort of one-time strike on inflation but a kind of persistent shock. The main policy implication is that if we want to influence inflation in a certain future month, then we should take a policy action seven months before the targeted period. On the other side, if we want to evaluate the effectiveness of a monetary policy action taken in any previous month, we have to assess it in the seventh month ahead.