When the cohomology ring of a generalized Bott manifold with Q-coefficient is isomorphic to that of a product of complex projective spaces CP^<n_<i>> , the generalized Bott manifold is said to be Q-trivial. We find a necessary and sufficient condition for a generalized Bott manifold to be Q-trivial. In particular, every Q-trivial generalized Bott manifold is diffeomorphic to a Π_<n_<i> > 1> CP^<n_<i>> -bundle over a Q-trivial Bott manifold.