A 40-channel superconducting quantum interference device (SQUID) system was constructed for measuring neuromagnetic fields. Main features of the system are the use of double relaxation oscillation SQUIDs (DROSs), and planar gradiometers measuring magnetic field components tangential to the head surface. The DROSs with high flux-to-voltage transfers enabled direct readout of the SQUID output by room-temperature dc preamplifiers and simple flux-locked loop circuits could be used for SQUID operation. The pickup coil is an integrated first-order planar gradiometer with a baseline of 40 mm. Average noise level of the 40 channels is around 1.2 $fT/cm/{surd}Hz$ at 100 Hz, corresponding to a field noise of 5 $fT/{surd}Hz$, operated inside a magnetically shielded room. The SQUID insert was designed to have low thermal load, minimizing the loss of liquid helium. The constructed system was applied to measure auditory-evoked neuromagnetic fields.