We study optimal monetary policy in a New Keynesian model in which the monetary authority faces a trade-off between inflation and output-gap stabilization due to cost-push shocks. In particular, we highlight the role of the inflation target adjustment in stabilization policy by showing that it can mitigate this policy trade-off and considerably improve welfare. The main findings can be summarized as follows. First, we find that the welfare cost of a standard Taylor rule is non-trivial, even with optimized policy coefficients. Second, we propose an additional policy tool of a medium-run inflation target (MRIT) rule. When combined with the standard Taylor rule, the optimal MRIT significantly reduces fluctuations in inflation originating from the cost-push shocks and results in a similar level of welfare to that associated with the Ramsey optimal policy. Third, the optimal MRIT needs to be adjusted in a persistent manner and in the opposite direction to the realization of a cost-push shock. Fourth, the welfare implication of the MRIT is more pronounced under a flatter Phillips curve. Finally, the main findings are relevant to the current economic environment of low inflation rates under a flat Phillips curve, implying that the monetary authority should increase the inflation target in such an environment.