Abstract The narrow‐band cooling of ion motion in the trap of a Fourier transform ion cyclotron resonance mass spectrometer (FTICR) using an external parallel resonant circuit is considered. The parameters of the circuit necessary for effective cooling of both axial and cyclotron ion motion are estimated. It is shown that the use of a resonant circuit may be helpful in studying the highly charged heavy ions produced in experiments with electrospray ionization combined with FTICR.