Using a Fr?hlich Hamiltonian for the electron-lattice interaction, an expression for the Peierls phase transition temperature( TP)of metallic helical carbon nanotube (n1,n2)has been derived. As an illustration, the formula is used to estimate TP of metallic(n1,n2). The results indicate metallic(n1,n2)are stable against the Peierls distortion and preserve metallic property at and far bellow room temperature.