A sensitive superconducting gravity gradiometer has been constructed and tested. Coupling to gravity signals is obtained by having two superconducting proof masses modulate magnetic fields produced by persistent currents. The induced electrical currents are differenced by a passive superconducting circuit coupled to a superconducting quantum interference device. The experimental behavior of this device has been shown to follow the theoretical model closely in both signal transfer and noise characteristics. While its intrinsic noise level is shown to be 0.07 E ${\mathrm{Hz}}^{\ensuremath{-}\mathrm{\textonehalf{}}}$ (1 E\ensuremath{\equiv}${10}^{\ensuremath{-}9}$ ${\mathrm{sec}}^{\ensuremath{-}2}$), the actual performance of the gravity gradiometer on a passive platform has been limited to 0.3-0.7 E ${\mathrm{Hz}}^{\ensuremath{-}\mathrm{\textonehalf{}}}$ due to its coupling to the environmental noise. The detailed structure of this excess noise is understood in terms of an analytical error model of the instrument. The calibration of the gradiometer has been obtained by two independent methods: by applying a linear acceleration and a gravity signal in two different operational modes of the instrument. This device has been successfully operated as a detector in a new null experiment for the gravitational inverse-square law. In this paper we report the design, fabrication, and detailed test results of the superconducting gravity gradiometer. We also present additional theoretical analyses which predict the specific dynamic behavior of the gradiometer and of the test.