Based on the Computer Simulation Technology (CST) software, numerical simulations are carried out for a higher-order multi-modes operation of a coaxial Bragg structure at a frequency of 100 GHz. Results confirm that the band-gap overlap of the spurious modes with the operating mode can be efficiently separated by setting the phase difference between the outer-conductor and inner-rod corrugations to be π, and that the residual side-lobes can be entirely eliminated by applying Blackman-window distribution to both the outer-conductor and inner-rod corrugations.