This work presents the current oscillation phenomena observed in an electrochemical Cu/0.5 M CF3COOH system. The dynamical response of this new oscillator was followed by both current density-potential (j-E) and current density-time (j-t) curves. The current oscillation phenomena of the investigated system were monitored over various potential scan rates and constant applied potentials as control parameters. The increase of potential scan rate significantly decreases both the potential range of current oscillations and the frequency of oscillations. At the j-t curves both the simple and the complex (period adding) oscillations were found. Moreover, with the increase of applied potential, the increase of period of oscillations and current oscillation amplitudes were observed. It appears that the period of current oscillations exponentially grows with applied potential.