The Rhodotron is a compact and highly efficient accelerator. This accelerator requires an electron gun with high repetition frequency, short pulses and low emittance, to ensure optimal acceleration performance. This paper shows the physical design, simulation, prototype development and beam testing of such an electron gun. The electron gun is designed as a grid-controlled electron gun based on a barium-tungsten thermionic cathode. The electron gun adopts a Pierce structure. It has a cathode voltage of -40 kV, an operating repetition frequency of 10.75 MHz, a design emission current of 200 mA maximum, and a single minimum pulse length of 3 ns. In the actual test, the electron gun measured a peak emission current of 204 mA with the cathode heater operating at 0.95 A/6.7 V, loaded cathode DC voltage -40 kV, and gate control voltage 290 V/10 MHz. When the beam pulse length is 2.7 ns, the beam current amplitude is 39.2 mA, and the actual beam emittance is less than 2 mm mrad. This result meets the design and accelerator application requirements.