Let [Formula: see text] be a prime number. For a number field [Formula: see text], let [Formula: see text] be the compositum of all [Formula: see text]-extensions of [Formula: see text]. Then Greenberg’s generalized conjecture (GGC) claims that the unramified Iwasawa module [Formula: see text] is pseudo-null over the Iwasawa algebra associated to the Galois group of [Formula: see text]. In this paper, we establish sufficient conditions of GGC when [Formula: see text] is a complex cubic field and give many examples which satisfy the conditions with the help of computer programs.