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The design of a W-band third harmonic gyrotron operating at the TE6,1 mode is presented. The low order whispering gallery mode TE6,1 is chosen as the operating mode for the purpose of suppressing mode competition with lower harmonic modes. And an iris resonator is used in order to lower the start current of the third harmonic mode. The numerical simulation results show that a single mode third harmonic radiation with power of 16 kW can be expected at a beam voltage of 45 kV and current of 3 A, and magnetic field 1.19 T, corresponding to the electronic efficiency of 12%.