A statistical method for the ion configuration probability distribution in non-LTE plasmas based on the average-ion model is described. In this method, the ion configuration probabilities are obtained from the average level population probabilities of the ions according to the binomial distribution. The non-equilibrium ion configuration distribution and X-ray spectra emitted from Au plasmas produced by 1.06 μm laser are studied. The calculated X-ray emission spectra are in the same energy band range as the experimental results. We discuss the non-equilibrium characteristics of X-ray emission, and show that the contributions of the multiply excited ions to X-ray emission are important.