In speech signals processing, speech signals are collected by microphones, and then use algorithms to extract and separate, ICA (Independent component Analysis, ICA) algorithm is in common use.When the number of microphone is less than speakers number, that is called underdetermined, then speech signals’ extraction needs overcomplete ICA algorithm . A two-step approach is introduced:geometric algorithm to estimate a mixing matrix and shortest path to estimate sources. The algorithm of speech signal extraction is very good, the simulation results verify the results.