In order to improve the efficiency and obtain high output power with pure mode, 3-D particle-in-cell simulations are made on a novel coaxial triode vircator. Simulation results show that due to the appearance of the additional cylindrical cathode rod along the centerline, pure TM01 mode can be obtained in the output region. Simulation results also show that high-efficiency and pure TM01 mode output maintains even for output waveguide radius (equals anode radius) somewhat larger than the cutoff radius of the TM02 mode ( $R_{c,\mathrm {TM02}}$ ). When the cathode and anode gap keeps unchanged, most optimal structure values can be scaled for models with different anode radius. By careful optimizations, the efficiency can reach 15% at an output power of 1.7 and 2.2 GW, respectively, for anode radii equal 5.6 and 6.6 cm ( $< R_{c,\mathrm {TM02}}$ ); For anode radii equal 7.6 and 8.6 cm ( $> R_{c,\mathrm {TM02}}$ ), the efficiency is about 13% at an output power of 2.5 and 2.9 GW, respectively. The operating frequencies all are about 3.6 GHz.