We have invented a three superconducting quantum interference device (SQUID) gradiometer (TSG) that uses three SQUID magnetometers and a novel feedback method to measure magnetic field gradients. One SQUID, designated the reference SQUID, operates normally except that its feedback loop output is directed to all three SQUIDs through identical nonsuperconducting coils around each SQUID. The feedback loops for the remaining two SQUIDs, the sensor SQUIDs, measure the differences between the magnetic field at the reference SQUID location and those at the sensor SQUID locations. The voltage difference between the two sensor SQUID outputs divided by the gradiometer base line, the distance between the sensor SQUIDs, represents the average magnetic field gradient. We have measured gradient sensitivities of 10−12 and 10−10 T/m√Hz for TSGs made from bare low‐Tc and high‐Tc SQUIDs. An advantage of a TSG is that a sensitive gradiometer, free of hysteresis error, can be made using relatively small substrates.