Single crystalline nano-sized multiferroic BiFeO3 (BFO) powders were synthesized through simple chemical co-precipitation method using polyethylene glycol (PEG) as capping agent. We obtained pure phase BiFeO3 powder by controlling pHand calcination temperature. From X-ray diffraction studies the nanoparticles were unambiguously identified to have a rhombohedrally distorted perovskite structure belonging to the space group of R3c. No secondary phases were detected. It indicates single phase structure. EDX spectra indicated the appearance of three elements Bi, Fe, O in 1:1:3. From the UV-Vis diffuse reflectance spectrum, the absorption cut-off wavelength of the BFO sample is around 558nm corresponding to the energy band gap of 2.2 eV. The size (60-70 nm) and morphology of the nanoparticles have been analyzed using transmission electron microscopy (TEM).   Linear M−H behaviour and slight hysteresis at lower magnetic field is observed for BiFeO3 nanoparticles from Vibrating sample magnetometer studies. It indicates weak ferromagnetic behaviour at room temperature. From dielectric studies, the conductivity value is calculated from the relation s = L/RbA Sm-1 and it is around 7.2 x 10-9 S/m.