  We consider Calabi-Yau threefolds of Borcea-Voisin type over Q. They are
constructed from products of K3 surfaces and elliptic curves. We use concrete
K3 surfaces and discuss the automorphy of the Galois representations associated
to the Calabi-Yau threefolds. The moduli spaces of these Calabi-Yau threefolds
are Shimura varieties. Our result shows the existence of a CM point in the
moduli space. We also consider mirror symmetry of Calabi-Yau threefolds.
