  The Maxwell extension of the conformal algebra is presented. With the help of
gauging the Maxwell-conformal group, a conformally invariant theory of gravity
is constructed. In contrast to the conventional conformally invariant actions,
our gravitational action contains the Einstein-Hilbert term without introducing
any additional (compensator) scalar field to satisfy the local scale
invariance. This is achieved by using the curvatures of the algebra. In a
special condition, we show that the resulting action is reduced to the
Brans-Dicke like theory of gravity. We subsequently find the generalized
Einstein field equation together with a coordinate dependent cosmological term
and additional contributions.
