In　order　to　extract　fetal　electrocardiogram　(FECG)　from　one　single　cutaneous　potential　recording　of　a　pregnant　woman,　we　propose　a　nonlinear　local　principal　component　analysis　(LPCA)　algorithm　to　extract　FECG.　Firstly,　based　on　the　theory　of　phase　space　reconstruction,　a　scalar　sequence　of　measurements　is　converted　into　state　vectors.　Secondly,　for　every　state　vector　in　local　area,　PCA　is　adopted　to　extract　mother　ECG　(MECG)　and　FECG.　Because　of　the　existence　of　noise,　it　is　better　to　adopt　PCA　for　the　second　time　to　extract　more　pure　FECG.　Simulation　results　show　the　effectiveness　and　robustness　of　the　algorithm.