Based on Taylor series expansion and curve fitting technique, a fast method to determine the node voltage was proposed. At the first stage, the pre-contingency voltage was calculated on the basis of Newton power flow approach, and the 1 to 3 order derivatives of voltage with respect to branch outage parameter were calculated by using the convergent power flow equation of the base network topology. Several points around the fault branch parameter could be obtained by using Taylor series expansion. At the second stage, the function of the node voltage with respect to the fault branch parameter was obtained by using curve fitting technique. The related parameters in the node voltage function were determined with four voltage equations. The advantage of the proposed method is that the coefficient matrix of various derivatives of node voltage with respect to the fault branch parameter is identical, and there is no need for the re-factorization of the coefficient matrix. The standard IEEE system analysis results have verified the correctness and fastness of the proposed method.