Ab initio calculations with MP3 and CISD method were performed for the FCO and $FCO^+$. The equilibrium geometry of FCO shows the reasonable agreement with experimental values. $FCO^+$ has a linear geometry with $R_{CF}=1.213;and;R_{CO}=1.118{AA}$. The quadratic force constants of $FCO^+$ are 23.21 md ${AA}^{-1}$ for CO stretch and 12.38 md ${AA}^{-1}$ for CF stretch. The cubic force constants and the other molecular constants are also calculated.