A novel white-light interferometric method based on window Fourier transform and cubic spline interpolation algorithm is proposed for accurate measurement of group delay dispersion of dispersive mirror applied in ultrafast laser system. Numerical simulations indicate that the proposed method exhibits precision up to 0.58 fs2. After analyzing the effect of Gaussian noise and averaging effect of light intensity on the test accuracy of the above method, home-made Gires-Tournois interferometer mirrors and chirped mirrors are measured. The experimental results demonstrate that group delay dispersion errors are less than 10 fs2 in a wide spectral range. It is concluded from numerical simulations and experimental results that the proposed method can obtain phase information of thin films correctly and quickly, and it is more precise and practical than other algorithms.