A new phase unwrapping method to extend the discontinuous wrapped phase with linear carrier before unwrapping is presented. First,the carrier frequency is determined by the Fourier transform method. Then the least-square method is used to calculate the linear carrier which matches with the wrapped phase to extend the background and obscurations region. Finally,the classical quality-guided method is used to unwrap the extended phase map. The experiment result shows that,for the discontinuous interferograms with large linear carrier,the unwrapping result avoids the global errors between different regions. The computer simulation result shows that,the method can be applied to discontinuous interferograms with small linear carrier or without carrier and get the correct unwrapping result can be obtained after linear carrier modulation.