In this paper, we derive the action for $N=3$ conformal supergravity in four
space-time dimensions. We construct a density formula for $N=3$ conformal
supergravity based on the super form action principle. Finally, we embed the
$N=3$ Weyl multiplet in the density formula to obtain the invariant action for
$N=3$ conformal supergravity. There are two inequivalent embeddings by changing
a particular coefficient from real to imaginary. They lead to invariant
actions, which will either be the supersymmetrization of the Weyl square term
or the Pontryagin density in the eventuality of gauge fixing to Poincar\'{e}
supergravity. As a consistency check of our formalism, we will show that the
supersymmetrization of the Pontryagin density is a total derivative. We will
demonstrate this for purely bosonic terms. We will also present the complete
action for the supersymmetrization of the Weyl square term. We also discuss
consistent truncation of $N=4$ Weyl multiplet to $N=3$ Weyl multiplet and use
it for a robust check of our results using the earlier known results in $N=4$
conformal supergravity.
