For sensitive measurements of micro-Tesla nuclear magnetic resonance (${mu}T$-NMR) signal, a low-noise superconducting quantum interference device (SQUID) system is needed. We have fabricated a liquid He dewar for an SQUID having a large diameter for the pickup coil. The initial test of the SQUID system showed much higher low-frequency magnetic noise caused by the thermal magnetic noise of the aluminum plates used for the vapor-cooled thermal shield material. The frequency dependence of the noise spectrum showed that the noise increases with the decrease of frequency. This behavior could be explained from a two-layer model; one generating the thermal noise and the other one shielding the thermal noise by eddy-current shielding. And the eddy-current shielding effect is strongly dependent on the frequency through the skin-depth. To minimize the loop size for the fluctuating thermal noise current, we changed the thermal shield material into insulated thin Cu mesh. The magnetic noise of the SQUID system became flat down to 0.1 Hz with a white noise of 0.3 $fT/{surd}Hz$, including the other noise contributions such as SQUID electronics and magnetically shielded room, etc, which is acceptable for low-noise ${mu}T$-NMR experiments.