  A cosmological model with perfect fluid and self-interacting quintessence
field is considered in the framework of the spatially flat
Friedmann-Robertson-Walker (FRW) geometry. By assuming that all physical
quantities depend on the volume scale factor of the Universe, the general
solution of the gravitational field equations can be expressed in an exact
parametric form. The quintessence field is a free parameter. With an
appropriate choice of the scalar field a class of exact solutions is obtained,
with an exponential type scalar field potential fixed via the gravitational
field equations. The general physical behavior of the model is consistent with
the recent cosmological scenario favored by supernova Type Ia observations,
indicating an accelerated expansion of the Universe.
