When using the Fourier transform method to demodulate the phase from an interferogram, the Gibbs effect often occurs at the edge of the phase picture. Fringe extrapolation is a straightforward method to suppress the Gibbs effect. Currently, many algorithms are used in fringe extrapolation, and exemplar-based methods are one such alternative. However, the traditional exemplar-based algorithm is based on the Criminisi algorithm, which is extremely time-consuming. In this study, the structure-guided image-completion method was applied to interferogram extrapolation. Simulations and experiments show that the new method reduces computer memory requirements and saves computing time. Compared with extrapolation using the Criminisi algorithm, the speed can be increased by tens or even hundreds of times.