Quintessence Cosmology with Coupled Real Scalar Field

In the light of the recent observations of type Ia supernovae (SNe Ia) suggesting an accelerating Universe, we show the possibility of a coupled real scalar field to be quintessence for the source of the accelerating Universe. We derive the main equations which govern the evolution of the Universe and rewrite them with the observable quantities. Finally we point out very briefly how future observations may determine the equation of state of quintessence.