In renal medicine, Estimated Glomerular Filtration Rate (eGFR) based method is a standard for the diagnosis of chronic kidney disease. However, this method is invasive, uncomfortable, costly, and could be dangerous because it requires to draw blood from the artery vessels. Researchers have developed several non-invasive Doppler-derived measures based chronic kidney disease (CKD) stage diagnosing or prognosing approaches; however, there is no adequate automatic renal artery Doppler-derived CKD stage classification method in the literature. Thus, we propose a non-invasive, safer, faster, and low cost, SVM-based CKD stage classification method from a sonogram of the renal artery blood flow. The proposed method extracts kurtosis and curvature parameters of the probability distribution that generated from renal artery blood flow waveform. Kurtosis and curvatures are employed to measure the tailedness and curvedness of the probability distribution. We collected a total of 528 sonograms from 110 (49 males) CKD patients during 2010-2013. The experimental results revealed a statistically significant correlation between the parameters and CKD progress stages. Post-voting results revealed the best f1score of 0.956 for Positive (stages 1-5) CKD stages.