Interferogram noise reduction is a very important processing step in Interferometric Synthetic Aperture Radar(InSAR) technique. The most difficulty for this step is to remove the noises and preserve the fringes simultaneously. To solve the dilemma, a new interferogram noise reduction algorithm based on the Maximum A Posteriori(MAP) estimate is introduced in this paper. The algorithm is solved under the Total Generalized Variation(TGV) minimization assumption, which exploits the phase characteristics up to the second order differentiation. The ideal noise-free phase consisting of piecewise smooth areas is involved in this assumption, which is coincident with the natural terrain. In order to overcome the phase wraparound effect, complex plane filter is utilized in this algorithm. The simulation and real data experiments show the algorithm can reduce the noises effectively and meanwhile preserve the interferogram fringes very well. Interferogram noise reduction is a very important processing step in Interferometric Synthetic Aperture Radar (InSAR) technique. The most difficulty for this step is to remove the noises and preserve the fringes simultaneously. To solve the dilemma, a new interferogram noise reduction algorithm based on the Maximum A Posteriori (MAP) estimate is introduced in this paper. The algorithm is solved under the Total Generalized Variation (TGV) minimization assumption, which exploits the phase characteristics up to the second order differentiation. The ideal noise-free phase consisting of piecewise smooth areas is involved in this assumption, which is coincident with the natural terrain. In order to overcome the phase wraparound effect, complex plane filter is utilized in this algorithm. The simulation and real data experiments show the algorithm can reduce the noises effectively and meanwhile preserve the interferogram fringes very well.