We designed and fabricated a new type of superconducting quantum interference device (SQUID) susceptometers for magnetic imaging of quantum materials. The 2-junction SQUID sensors employ 3D Nb nano-bridges fabricated using electron-beam lithography. The two counter-wound balanced pickup loops of the SQUID enable gradiometric measurement and they are surrounded by a one-turn field coil for susceptibility measurements. The smallest pickup loop of the SQUIDs were 1 μm in diameter and the flux noise was around 1 μФ0/√Hz at 100 Hz. We demonstrate scanning magnetometry, susceptometry and current magnetometry on some test samples using these nano-SQUIDs.