This paper presents a design of spiral antenna with broad bandwidth for non-linear junction detector(NLJD). An elliptical patch as radiating element located on center position of radiating surface, as well as the spiral elements on radiating surface was designed for broad bandwidth of spiral antenna. An antenna ground structure generating the multi resonance by spiral slit inserted on ground surface was also proposed. In order to realize high directivity and high gain of the proposed antenna, the cavity wall made of Fr4-epoxy and the metal cap were considered in design. As a result, the calculated gain of antenna with metal cap was improved about 3 dB with comparison of antenna without metal cap and the measured main beam directivity toward -z axis direction agreed well with calculation result. The measured axial ratio satisfied the circular polarization within -z axis ${pm}45^{circ}$ at design frequency bands and showed reasonable agreement with prediction.