This paper investigated how sensitive food price is to changes in petroleum price and exchange rate in Ghana from January 1997 to August 2017. Interest rate was included as a control variable in the study since it may be a useful macroeconomic policy tool. Using Johansen cointegration procedure, Vector Error Correction Model, Impulse Response Functions and BEKK-GARCH estimations, the results of the study showed there exist positive long-run and short-run relationships between food prices and all the macroeconomic variables used in the model. Thus, increases in petroleum price, exchange rate and interest rate raise food prices in Ghana. The magnitudes of these increases were found to be very high during the food crises periods in 2007/08 and 2010/11. It was also found that effects of these food price spikes caused by shocks from petroleum price, exchange rate and interest rate are long lasting and do not decay easily with time. The results from the BEKK-GARCH estimation showed that food prices in Ghana exhibit time-varying volatility; caused by its own ARCH and GARCH effects as well as exogenously determined shocks from petroleum price, exchange rate and interest rate. Also, the results indicated that food price volatility shocks in Ghana are persistent. It is recommended that; policy aimed at food price stabilization must build national petroleum buffer stocks to stabilize fuel prices, improve exchange rate and interest rate management, build district, regional and national food buffer stocks, selectively target fuel subsidy at crop farmers and food processors, and remove bottlenecks in food marketing.