To measure transparent parallel plates more easily and accurately, a phase recovery method based on the region growing algorithm and Fourier transform for single three-surface interference fringes was proposed. Through the Fourier transform, the three-surface interference fringe pattern was changed from the spatial to the spectral domain. Because the interference fringes of different surfaces have different positions in the spectral domain, the appropriate regions were extracted by changing the parameters in the region-growing algorithm, and the final surface was obtained. By this method, the planar shapes of the front and rear surfaces of the transparent parallel plate can be simultaneously obtained from a single three-surface interference fringe pattern. From an error analysis of the surface shapes obtained by the algorithm, a superimposed and separated double-surface interferogram was compared with the original three-striped graph to obtain the corresponding error distribution graph. The accuracy of the algorithm was improved through the error distribution graph. A comparison of the obtained surface shapes with that obtained by a Zygo interferometer reveals that the method had high measurement accuracy with a phase extraction error PV value of less than 0.12λ and a Root Mean Square(RMS) value of less than 0.065λ. A verification of the repeatability shows that the repetition rate is reliable, and the degree is better than λ/100. The measured surface shape approximated the real surface shape of the object, and the measurement method proved to be simpler than the original method.