  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 superform action principle. Finally, we embed the N =
3 Weyl multiplet in the density formula to obtain the invariant action for N =
3 conformal supergravity. We will show that 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. 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.
