The nano-size effects of high-Tc cuprate superconductor La2−xSrxCuO4 with x = 0.20 are investigated using X-ray diffractometry, Transmission electron microscopy, and muon-spin relaxation (μSR). It is investigated whether an increase in the bond distance of Cu and O atoms in the conducting layer compared to those of the bulk state might affect its physical and magnetic properties. The μSR measurements revealed the slowing down of Cu spin fluctuations in La2−xSrxCuO4 nanoparticles, indicating the development of a magnetic correlation at low temperatures. The magnetic correlation strengthens as the particle size reduces. This significantly differs from those observed in the bulk form, which show a superconducting state below Tc. It is indicated that reducing the particle size of La2−xSrxCuO4 down to nanometer size causes the appearance of magnetism. The magnetism enhances with decreasing particle size.