  In this paper, we use the superconformal approach to derive the higher
derivative 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.
