  We describe explicitly the chamber structure of the movable cone for a
general smooth complete intersection Calabi-Yau threefold $X$ of Picard number
two in certain Pr-ruled Fano manifold and hence verify the Morrison-Kawamata
cone conjecture for such $X$. Moreover, all birational minimal models of such
Calabi-Yau threefolds are found, whose number is finite up to isomorphism.
