Presented in this paper is a conceptual design by computer simulation of a monopulse reflector antenna with dual-circularly polarized sum patterns and linearly polarized azimuth and elevation difference patterns, which can be called a semi-dual polarized antenna. The proposed antenna consists of a five-element monopulse feed and a prime-focus parabolic reflector. The novelty of the proposed antenna is a monopulse feed consisting of a dual-circularly polarized square waveguide sum channel radiator and linearly polarized rectangular waveguide azimuth and elevation difference channel radiators. The separation of dual circular polarization is realized by a septum polarizer. The difference pattern is obtained by feeding two rectangular waveguides in opposite directions using a coaxial probe. The proposed monopulse feed geometry requires only two power combiners for a monopulse comparator network while providing dual-polarized performance comparable to the full dual-polarized sum and difference channel monopulse scheme. The concept of the proposed antenna is shown in a conceptual design by computer simulation. The monopulse feed is designed first, and then combined with a parabolic reflector. The designed monopulse reflector antenna operates at 14.5–16.0 GHz, and shows excellent sum and difference pattern characteristics: 36.1–36.7 dBc sum channel directivity with 0.65 dB boresight axial ratio and 32.6–32.9 dBi difference channel directivity with 1.56–1.66° crossover angle.