Bankruptcy Prediction has been a popular topic in business area. Once the firm goes bankrupt, it will bring the great loss to not only firm itself but also other stakeholders. The widely applied methods to predict the risk of business failure were based on financial ratio analysis; in which, applying Grey System Theory in the previous thesis for predicting default probability of construction firms, has brought some feasibility results, by relying on the 19 initial financial ratios. With the purpose of improving the Grey System Theory application, in this thesis, the authors would like to reduce the number of financial ratio before applying Grey System Theory, and then the results will be compared with previous thesis. First, the Logistic Regression model, an accounting – based Model was applied to filter out the most important variables, before applying Grey Theory. Then, Synthetic Degree Incidences ρ of considered firms are calculated and combine these ρ values, the default probability of firms will be identified. Then, the other effected factors like as X zero (X0), theta θ and the key variables were considered. After that, using ROC curves to point out which one is the most favorable consequence data for model (correspond to the highest AUC value). Lastly, some comparisons as well as recommendations are suggested.