A novel SQUID vector magnetometer system is introduced which has been specially designed for the use inside the strongly magnetically shielded room BMSR-2 of PTB. The system is housed in a dewar with a flat bottom and an inner diameter of Ø 250 mm. The SQUIDs are arranged so that in addition to the usually measured Z-component of the field the horizontal magnetic fields are measured too. A total of 304 DC-SQUID magnetometers are divided up into 19 identical modules. The 16 low-Tc SQUIDs of each module are located in such a way that an estimation of the magnetic field in all three dimensions is possible at three points inside the module. The 57 SQUIDs of the lowest Z plane of all modules form a hexagonal grid with a base length of 29 mm. The design criteria and the physical principle behind the complex SQUID arrangement are explained.