A novel type of acoustic resonance different from the well-known Bragg resonance is predicted theoretically in an acoustic cylindrical waveguide with sinusoidally perturbed hard walls. The resonance is caused by the interaction between the standing acoustic waves, i.e. transverse modes in the waveguide. It results in the frequency spectrum splitting and the appearance of forbidden bands. For small-perturbed wall corrugation, it is found that the shifts of resonant frequencies and the width of the forbidden gap can be as small as the wall amplitude. The appearance of the non-Bragg resonance depends highly on the wall period. When the period is greater than 2.319 times the average cylinder radius, all the non-Bragg resonances cut off. The smaller the wall period, the greater the transverse mode involvement.