Based on the analyses and the calculations of the gyroklystron amplifiers self-consistent nonlinear theory, a scheme of Kα-band, TE01 mode, four-cavity fundmetal wave gyroklystron is designed.At the same time, a gyroklystron amplifier is made and tested. The hot test experiment shows that the gyroklystron amplifier can produce 245 kW peak output power, and 3 kW average power at a 35% efficiency and saturated gain of 36.1 dB at central frequency 34 GHz, when using 60 W driving power, and a 70 kV, 10 A annular electron beam in a magnetic field of 1.31 T. The full width half maximum (FWHM) bandwidth is higher than 280 MHz. The amplifier is zero-drive stable. Experimental results are found to be in excellent agreement with theoretical predictions.