Abstract: To accurately calculate the frequency response of transformer winding equivalent circuit is the basis for studying frequency response analysis（FRA）simulation method. The sparse tableau method is investigated for calculating the FRA curves of equivalent circuit of two-winding transformer. Firstly,based on the graph theory and the relationship between branch voltage,branch current and the constraints of electrical components,the sparse tableau equation of the equivalent circuit is constructed. Then,the FRA curves with different FRA test connections are obtained by solving the equation. Finally,the accuracy of the proposed method is validated through case analysis. This method can obtain the branch voltage vector,branch current vector,and the node voltage vector at the same time only by solving the sparse tableau matrix once. It avoids the multiple matrix solution process caused by the change of test connections and it can rapidly get the FRA curves under different FRA test connections.