The dispersion curves of the coaxial slow-wave structure(SWS) with the trapezoidal corrugation are obtained by numerical calculation. The electric field vector of π mode of the quasi-TEM mode and the influence of the inner-conductor radius on resonance frequency are calculated using the electromagnetic software Superfish. In addition, a compact L-band relativistic backward wave oscillator(RBWO) is investigated and optimized in detail with particle-in-cell(PIC) methods(Karat code) to explain effects of the inner-conductor radius. In experiment, the operation frequencies are 1.64 GHz, 1.63 GHz and 1.61 GHz when the inner-conductor radii are 0.50 cm, 0.75 cm and 1.00 cm respectiuely, which shows that the operation frequency decreases with the enlargement of the inner-conductor radius. To sum up, the experimental results are in good agreement with the results of the theoretical analysis.