Precise band-filling control is performed on a strongly correlated electron system Na x CoO 2 , by changing the Na content, and the influence of this on the magnetic and thermodynamic properties is studied. It has been discovered that a phase boundary between a Pauli paramagnetic metal appearing at small x and a Curie-Weiss metal at large x is located within an extremely narrow range of 0.620Ͻ x Ͻ 0.621. The transition between these is a Lifshitz transition of the pocket-vanishing type, exceptionally achieved by band-filling control. Abrupt changes in various properties across the boundary are remarkably observed, suggesting that the Lifshitz transition occurs discontinuously in Na x CoO 2 , differently from the conventional Lifshitz transition defined at T =0.