For all the present phase unwrapping algorithms,it is still a tough question to obtain an accurate unwrapping phase from interference fringes which suffer from enormous under-sampling and c an be affected by the background noise. To solve this problem,a new phase unwrapping algorithm based on k round is proposed for recovering wrapped phase with enormous undersampling and background noise.The new phase unwrapping algorithm is improved by shearing interferometry and advanced iterati on algorithm.On the one hand, the ability of processing the wrapped phase can be improved.On the other hand, it accelerates the running speed of the program.The running time of the new phase unwrapping algorithm is approxima tely equal to that of discrete cosine transform (DCT).The phase wrapped coefficient k round method is also introduced into the new phase unwrapping algorithm,which can unwrap the phase more accurately and increase noise immunit y.Comparing with other least-square methods,the proposed algorithm demonstrates better performance.The results show that the method not only can recover undersampling wrapped phase,but also has strong noise immunity.