For the study of the Sigma resonances, we analyze the differential cross sections and Lambda polarizations for the reactions K- n -> pi(-) Lambda and K- p -> pi(0)Lambda with an effective Lagrangian approach. Data of an early experiment and the recent Crystal Ball experiment at BNL are included in the analysis with the c. m. energy from 1550 to 1676 MeV. Our results clearly support the existence of a Sigma resonance with J(P) = 1/2(+), mass near 1633 MeV, and width about 120 MeV, which confirms the three-star Sigma(1660)1/2(+) in PDG. Meanwhile, our results do not support the existence of the two-star Sigma(1620)1/2(-) in PDG. The analysis results for the parameters of the relevant Sigma resonances and couplings are presented.