Both Newton's method and homotopy continuation method belong to the algebraic computation methods. It is crucial to supply the appropriate initial values for Newton's method in order to solve the multi-solution problem successfully. Based on the research on the two computation methods， it is found that: if points 1-0 and 0-0 are chosen as the fixed points and based on which the fixed-point homotopy functions are built， the values of the state variables can be solved by the initial value computation; then the values of state variables can be considered as the initial iterative values of Newton's method， and the convergence of the computation process can be assured by shifting the positions of the fixed points. Similarly the high voltage or low voltage equilibrium points of the system can be calculated quickly in the case of heavier loads. The improved homotopy continuation method reduces computational costs on calculating the homotopy curve as the classical homotopy continuation method does and prevents the values of the state variables from approaching infinity. The linearly independent equations are structured by the solved pairs of equilibrium points to define the coefficients of the fitting curve for QV curve and the position of the stability limit point can be obtained. The accuracy of the method meets the engineering requirement and it takes less computation time. It is applied to analyze some network structure preserving models and the analysis results are satisfactory.