The gyroklystron is a high power, high gain, and high efficiency millimeter wave amplifier. Its circuit usually comprises of 4 or 3 stagger-tuned cavities. The input coupler is the first cavity of the circuit and must exhibit reasonable coupling strength between the TE10 mode in rectangular waveguide and the desired TE011 or TE021 circular cavity mode with high purity. The theoretical analysis and HFSS simulation of the input coupler are presented. Mode matching technology is used to calculate the size of coaxial and cylindrical cavities. A new method, combining theory and HFSS, is presented to calculate the purity of working mode. Some results are obtained through the study of the orientation, width and length, angular offset of the apertures. The results show that 45°orientation is bett