Both undoped and Cr doped ZnO nanoparticles with composition of $Zn_{1-x}Cr_xO$ ($x = 0, 0.02, 0.04, 0.06, 0.08$) were prepared by co-precipitation method. These nanoparticles were characterized by using thermogravimetry for identification the calcination temperature. X-ray diffraction, transition electron microscope, Fourier transform infrared spectroscopy. X-ray diffraction patterns of all the samples displayed peaks of a hexagonal wurtzite structure. The structural properties investigated by X-ray diffraction revealed hexagonal wurtzite ZnO type structure. Both XRD and TEM were shown that the crystallite size of the nanoparticle decreases with increasing Cr content. In addition, the magnetic properties as a function of chromium concentrations was studied. $Zn_{1-x}Cr_xO$ ($x = 0.02, 0.04, 0.06, 0.08$) nanoparticles have a ferromagnetic behavior.