In this paper, we propose a non-parametric approach for comparing diagnostic accuracies in multi-reader receiver operating characteristic (ROC) studies. The approach constructs a test from each reader by extending the conventional non-parametric method and then combines all the individual test statistics to draw an overall conclusion on the relative accuracies of different diagnostic tests. The method can handle both continuous and ordinal data. Compared to the existing non-parametric methods, the method is robust and effectively deals with the possible heterogeneity among readers. It can also be applied to the analysis of correlated ROC studies. The method is applied to a real example and its finite sample performance is examined through simulation studies.