In this paper, we use the superconformal approach to derive the action for N
= 3 Poincare supergravity in four space-time dimensions. We first study the
coupling of N = 3 vector multiplets to conformal supergravity. Thereafter we
combine it with the pure N = 3 conformal supergravity action and use a minimum
of three vector multiplets as compensators to arrive at Poincare supergravity
with higher derivative corrections. We give a general prescription on how to
eliminate the auxiliary fields in an iterative manner and obtain the
supergravity action order by order in derivatives. We also show that the
truncation of the action at fourth order in derivatives is a consistent
truncation.Comment: 31 pages,minor change