Low-noise, high-stability current sources have essential applications such as neutron electric dipole moment measurement and high-stability magnetometers. Previous studies have mainly focused on frequency noise above 0.1 Hz while less on the low-frequency noise/drift. This paper use double resonance alignment magnetometers (DRAMs) to measure and suppress the low-frequency noise of a homemade current source (CS) board. The CS board noise level is suppressed by about 10 times in the range of 0.001 Hz - 0.1 Hz and is reduced to 100 nA/$\sqrt {{\rm{Hz}}} $ at 0.001 Hz. The relative stability of CS board can reach 2.2 × 10-8. Besides, the DRAM shows a better resolution and accuracy than the commercial 7.5-digit multimeter when measuring our homemade CS board. Further, by combining the DRAM with a double resonance orientation magnetometer, we may realize a low noise CS in the 0.001 Hz -1000 Hz range.