A device to detect small vibrations, which we call a flux gradient accelerometer, has been constructed. We propose to use such a device as the transducer for a low‐temperature gravitational wave detector. The accelerometer is found to respond as predicted by a simple harmonic oscillator model with a sensitivity nearly equal to the sensitivity calculated theoretically. If the accelerometer signal were amplified by a SQUID (superconducting quantum interference device) having a flux noise of 1.4×10−12G cm2 Hz−1/2, the signal should just equal the noise when &Dgr;xrms=9×10−18(&Dgr;f)−1/2cm where &Dgr;xrmsis the rms displacement, and &Dgr;fis the amplifier bandwidth.