The grain size dependence of magnetic properties of the mother material of the high-Tc cuprate, La2CuO4 (LCO), is proposed to study by muSR. Although LCO shows an antiferromagnetic (AF) ordered state below about 270 K, the AF state could change or disappear when the grain size of LCO becomes to be in the nano-scale order, like a couple of ten nano-meters. Controlling the grain size of LCO , we plan to clarify whether the AF state really disappears or not in the nano-scale LCO.