Distribution of magnetic field inside the solenoidal coil is calculated by using Simpson algorithm. It is proved that the off-axis magnetic field can be used for bunching the electron beam. With the aid of 2D particle-in-cell code, an X-band five-cavity high-gain klystron amplifier is designed with an output power of 299.46 MW, a frequency of 9.45 GHz, a gain of 50.3 dB and an efficiency 37.4% respectively. Three-dimensional model of device placed on the coil central axis and off-axis is designed. And the simulation result demonstrates that the off-axiss device can amplify microwave signal. Seven tubes are placed inside one solenoidal coil simultaneously, the simulated result shows that synthetic power can reach 2 GW theoretically.