Charge-exchange collisions between ultracold fermionic
6Li atoms and
40Ca+ ions are observed in the millikelvin temperature range. The reaction product of the charge-exchange collision is identified via mass spectrometry during which the motion of the ions is excited parametrically. The cross sections of the charge-exchange collisions between
6Li atoms in the ground state and
40Ca+ ions in the ground and metastable excited states are determined. Investigation of the inelastic collision characteristics in the atom-ion mixture is an important step toward ultracold chemistry based on ultracold atoms and ions.