A new monopulse antenna is designed and analyzed based on quasi-optical technology at sub-millimeter wavelengths. The radiation performances of the proposed monopulse antenna are rigorously investigated by combining the Finite Difference Time Domain(FDTD) method and the Stratton-Chu formula. In order to suppress the side lobe levels of sum radiation patterns, a modified hyperbolic-plano dielectric lens with cutting segments is introduced. The simulated results show that this monopulse dielectric lens antenna has good radiation characteristics with the side lobe levels below -11.9 dB in sum patterns, the maximum null-depth below -30.0 dB and the amplitude imbalance below 0.50 dB in difference patterns.