This paper describes a design for a spiral antenna with a conical wall to obtain the high gain. The gain and the axial ratio of the spiral antenna were improved by a new design that included a conical wall and an optimized Archimedean slit on the ground plane in a conventional antenna with a circular cavity wall and a 4.5-turn slit. A gain improvement of 9.5 dBi higher and a good axial ratio of 1.9 dB lower were measured by the added conical wall and the newly designed slit from the current distribution control on the ground plane, respectively. The measured return loss, gain and axial ratio of the proposed antenna showed a good agreement with the simulated results. The proposed antenna will be applied to a non-linear junction detector system.