The TE6,11 mode has been selected as a candidate for the second harmonic operation of a terahertz gyrotron at 1007.68 GHz. The predicted efficiency is 8.6 percent for the output power 0.38 kW. Time-dependent, multi-mode calculations have been carried out to investigate stability of a single-mode operation at second harmonic. It has been found that with the beam current 0.111 A and the magnetic field 19.282 T the second harmonic operation in the TE6,11 mode is possible.