We describe orientifold operation defining O3 plane in the conifold background by deriving it from that of O4 plane in the Type IIA brane construction by T-duality. We find that bothO3+andO3−are at the tip of the cone so that there is no net untwisted RR charge. RG analysis shows that we need two “fractional” branes for the conformal invariance in orientifolded conifold. We describe the deformation of the moduli space of the field theory in the presence of the orientifold. The finitely resolved conifold does not allow the orientifold, while deformed conifold leaves us an unresolved issue on supersymmetry. ©2002 American Institute of Physics.