Traditional adding one power integrator control(AOPIC) convergence speed is even slower than linear control if the states are far from origin. To solve this problem, based on the traditional AOPIC and fast finite time Lyapunov theorem(FFTLT), a fast adding one power integrator control(FAOPIC) method is proposed for a class of nonlinear systems with mismatched uncertainties and external disturbance, which has the advantages of the AOPIC and FFTLT. Then it is strictly proved that the FAOPIC can speed up the convergence process of AOPIC, which is just exponential convergent or non-fast finite time convergent at any point, and it has stronger robustness and smaller steady error. Simulations are conducted to verify that the proposed method has significant better performance than AOPIC, and is very suitable for engineering application.