The twinned sheets structure, which is believed that is heplful for its strength but harmful for its magnetostriction, generally exists in the micro structure of Terfeno-D. In order to prepare the twinned sheets free terfenol single crystals, a method of growth with magnetic levitation cold crucible in CZ(Czocharalski) technique has been explored successfully. In this paper, we will discuss the formation of the twinned sheets defects according to the pusedo binary phase diagram of R(Tb, Dy)--Fe and the crystallization beheavior of RFe2 Laves phase. Micro structures of the CZ terfenol crystals are observed by SEM techniques. The influences of growth conditions and precursor alloy compositions on the structures and magnetostriction of CZ terfenol single crystals alos have been consdiered.