Modulator cavity of multi-cavity Gyroklystron transforms the TE411 mode in out cavity to TE011 mode in inner resonant cavity through 4 slots. TE011 mode is used to modulate the transverse velocity of gyroelectron beam. In this paper, an analysis of cold cavity is presented. HFSS code is used to simulate couple of structure variety accurately and revise approximate analysis. It shows that the ratio of the energy storage of the inner cavity to that of the outer cavity is 41.65, when the angle between coupling slots' midline and waveguide axis is 45°. Length of slots affects Q factor greatly while resonance frequency is insensitive to it. Moreover, Q factor is more sensitive to length of slots than to width of them. Energy storage in coaxial cavity is calculated. Based on a large number of c