The phase transitions of a newly proposed torsion X-Y model, are studied with molecular dynamics. ForJ3 >0, the influence from J1 term is similar to the term.We found the Torsion X-Y Model and X-Y Model or Coupled X-Y Model all have the Kosterlitz-Thouless transition. (KT) We also confirm that the KT transition is a second order transition , The distribution of angle £c start from dis-ordered to well-ordered. KT starts first before the randomly distributed £c shows preference and ends when the preference is merged. For the J3 <0 case, the KT is also found in J3=-0.0167 and J3=-0.0334 The temperature for negative J3 is lower then that for positive J3 due to the resistant force to £c ordering from the coupled interaction.