Abstract: In this paper we present a design of a circular polarizer working in the K band.More specifically, it works in the frequency range of 18GHz to 26.5GHz.There are many important spectral lines in the K band, so that a design of a circular polarizer working in this band can highly significantly facilitate astronomical observation and scientific research.The circular polarizer is used to transform linearly polarized signals received by a feed to circularly polarized signals for the convenience of radio-telescope observation.We describe the principle, key aspects, simulation results, and other relevant issues about the design.Our descriptions mainly cover two important devices, the orthogonal mode transducer (OMT) and the phase shifter.The OMT is used to separate signals in modes orthogonal to each other, and the phase shifter is used to induce a phase difference of 90 degrees between signals of two such modes.By combining the two devices and a twisted waveguide of square cross sections and a twist angle of 45 degrees, we construct a K-band circular polarizer.Based on the principle and 3D electromagnetic simulations we specify the details of the design.Our simulations show that the losses of the OMT and phase shifter are both less than-20dB, and the error of phase shifting by the phase shifter is less than 3.3 degrees.We finally show some simulation results of the entire system of the circular polarizer.