The　low-field　pulsed　NMR　signal　is　interfused　by　noise　during　the　measurement.　It　is　important　to　reduce　noise　while　keeping　peaks　well.　This　paper　proposes　a　novel　wavelet　filtering　method　by　spatial　correlation　thresholding　based　on　UDWT　(Undecimated　wavelet　transform).　We　multiply　two　adjacent　wavelet　scales　with　some　relative　translations　to　line　up　the　edges.　A　new　threshold　is　also　presented　applying　to　spatial　correlation　in　our　proposed　scheme.　The　simulation　results　indicate　that　our　algorithm　can　keep　edges　well　while　removing　noise　greatly.　It　is　an　effective　noise　filtration　technique　especially　for　low-field　pulsed　NMR　signal.