The difference between fully ionized and partially ionized plasmas lies in the presence of bound electrons. From this difference the propagation of intense laser pulse and the refraction index in a partially ionized plasma are analyzed. An atomic filamentation instability (AFI) can be significantly enhanced by bound electrons. The AFI in Au plasma-produced 0.35 and 0.53 μm wavelength laser light to irradiate golden target are analyzed and calculated. The results show that the growth rate of the AFI is substantially higher than that of the relativistic filamentation instability.