A novel approximate continuation power flow algorithm is presented to realize voltage stability on-line monitoring. The method consists of two stages， viz. prediction and correction. The prediction algorithm linearizes power flow equations and predicts next step power flow solution along its tangent direction. The correction algorithm obtains calculative load increase direction by substituting the prediction solution into power flow equations. The algorithm uses the adjusted direction to predict power flow solution of next step， which can decrease the angle between load increase direction and calculative load increase direction. It is iterated until the angle is greater than a given value， which means that the linearization degree of power flow equation is deteriorated and the approximate load margin is obtained. Furthermore， in order to show the validity of the new algorithm in analyzing voltage stability， a strict mathematic proof is presented to show that this algorithm is linearization approximation of continuation power flow. The algorithm has a fast calculation speed and no convergence problem. Its voltage stability index has explicit physical meaning and good linearization property. Case studies using the IEEE 39-bus system are given to prove the effectiveness of the proposed algorithm.