The present work seeks to investigate the implications of following an inflation targeting regime under fiscal dominance. For this, a new Keynesian dynamic stochastic general equilibrium (DSGE) model is developed in which the monetary authority follows a Taylor rule with the objective of stabilizing inflation and output, and the fiscal authority follows a primary surplus rule, with The purpose of stabilizing public debt. This model is characterized by a coordination between the fiscal and monetary authorities in which monetary policy is dominant. Subsequently, the monetary rule is modified to incorporate a response of the monetary authority to the public debt and the fiscal rule becomes exogenous (active), characterizing a regime of fiscal dominance. Finally, the model is calibrated with the parameters estimated by De Castro et al. (2015) for the Brazilian economy and the inflation rate and output gap variances (proxies for the welfare losses due to economic fluctuations) are computed in the different regimes and under different specifications of the monetary and fiscal authorities reaction functions. It is shown that under a fiscal dominance regime, the monetary authority should not react aggressively to inflation. In other words, this means that if the Central Bank wants inflation to stay in it s target level - as it is required under an inflation targeting regime - it cannot in any way ignore the fiscal authority s stance.