The impacts of the inflation and the jumps on optimal asset allocations of an investor under asset prices with a jump environment are investigated． An investor allocates his assets to the risky asset and the riskless asset． First，we obtain the dynamics of consumer-basket-price with inflation by using It formula． Then，maximizing the expected utility of the terminal wealth discounted by inflation，and using the HJB equation，the optimal allocation strategy is obtained，and an approximate solution of the optimal dynamic asset allocation is given． Moreover，the inflation hedging demand and the effect of a jump on the myopic demand are discussed． Finally，we analyze the impacts of the jumps and inflation on the optimal allocation strategy of an investor through a numerical simulation．