An approach of unknown phase shifts extraction and complex wave reconstruction in generalized phase-shifting interferometry is proposed by the combination of least square methods and generalized four-step formulae. A much-simplified algorithm is suggested to extract reference phase and then reconstruct object wave-front by replacing the conventional least-square method in above process with our specially derived wave reconstruction formulae for generalized phase-shifting interferometry. In this method, only one least-square equation is needed for one iteration to retrieve the reference phase, and the object phase can be calculated simultaneously. The feasibility and effectiveness of this algorithm have been verified by computer simulations. The results show that this innovation can keep the phase extraction errors mostly in 0.004 rad and save computing time by about 10 times compared with previous four-step LSM algorithm while it still ensures its high precision. Optical experimental results are also satisfactory.