The resonant frequency of dielectric rod resonator can be calculated very accurately by means of the concept of electric and magnetic walls from the symmetry. But in a real situation, when the supporter is placed in the cavity, asymmetry appears due to the supporter and its dielectric constant. Then we need research into the resonance characteristic of asymmetric dielectric resonator. In this paper, for the dielectric rod resonator which is placed in the asymmetric position in the conducting cavity, the equation for resonance characteristic was derived and the resonant frequency was calculated with the eigenfunction expansion method. We found that the calculated resonant frequency is very accurate when it was compared with the experimental result and that asymmetry affects the resonant frequency more in TM mode than in TE or in hybrid mode.