This paper presents a general discussion of projective symmetry in FRW spac
etimes. It is shown that there is at most one proper projective vector fiel
d admitted in the sense that any other projective vector field is a linear
combination of the original and a homothetic vector field. The situation is
, essentially, solved completely for the FRW models with k = +/-1 and up to
quadratures in the case k = 0.