  Extended quintessence is obtained by coupling a normal scalar field to the
Ricci scalar defined in the metric formalism. In this paper, we propose a new
extended quintessence dark energy by introducing a non-minimal coupling between
the quintessence and gravity, but with the Ricci scalar given from the Palatini
formalism rather than the metric one. We find that the equation of state of the
new extended quintessence can cross the phantom divide line, and moreover, it
oscillates around the -1 line. We also show that the universe driven by the new
extended quintessence will enter a dark energy dominated de Sitter phase in the
future.
