A broadband terahertz quasi-optical detector has been developed with frequency from 140 GHz to 325 GHz. The terahertz quasi-optical detector consists of a silicon lens with high resistivity and a monolithic detector chip. A double slot antenna was fabricated on the chip with a Schottky diode assembled cross the terminals of the antenna. This compact structure endows the chip with the functions of receiving THz radiations from space and converts them into baseband. To improve the directivity of the antenna on chip, the hyper-hemispherical silicon lens was designed and optimized by MLFMM (Multilevel Fast Multipole Method)) algorithm, resulting in good radiation performance. The antenna gains at 220 GHz and 324 GHz was calculated to be 26 dB and 28 dB, respectively, from the measured radiation patterns. The measured responsivities of the detector achieve 1 000~4 000 V/W from 140 GHz to 325 GHz and the noise equivalent powers (NEP) were estimated to be 0.68~2.73 pW/Hz.