Continuous power flow (CPF) calculation is an important tool for power system analysis in studying static voltage stability and system transmission capacity. However, a critical point singularity seriously restricts the application and development of CPF. Therefore, the key to better application of CPF is to solve the problem of the critical point singularity. An improved Chord method is proposed to deal with the calculation of the critical point in the CPF problem. It can quickly calculate the solution at the critical point, and has fast convergence speed, reaching second-order convergence. It does not need to expand the original Jacobian matrix, so it does not need to worry about the problem that the nonsingular points in the original system become the singular points of the extended Jacobian matrix of the system. This makes the calculation process simpler. Applying the linearization method to predict the calculation direction of CPF, the whole calculation process is simple and convenient. Compared with the extended power flow method, the Chord method presented in this paper is simple and efficient. The simulation results of the IEEE 39-bus and IEEE 57-bus systems under different working conditions show that the proposed model and method can quickly and effectively calculate the singular solutions of CPF, and it has a good accuracy and robustness. This work is supported by the Key Special Fund of Smart Grid Technology and Equipment of National Key Research and Development Program of China (No. 2016YFB0900600).