This paper proposes an algorithm of rapidly determining the node voltage based on current and voltage compensation. The pre-contingency voltage is calculated by Newton power flow method, and the derivatives of first 2 orders of current and voltage with respect to branch outage parameters are calculated by using the convergent power flow equation of the base network topology. The values of current and voltage are obtained by using the Taylor series expansion. Lines out of operation(excluding the generator) based on the power injection remain unchanged, the node's current and voltage satisfy the compensation principle, the function of the node voltage with respect to the fault branch parameters is obtained by calculating the average compensation of current and voltage as the voltage Taylor expansion of the correction. The advantage of this method 1ies in the fact that the admittance matrix is not to be re-factorized after one branch is out of operation, and the accurate node voltage can be obtained by using only a low order Taylor expansion, to meet the requirements of calculation speed and accuracy. The feasibility and the efficiency of the proposed method are tested on the standard IEEE system.