In　advanced　wireless　communication　systems　that　require　spectrally　efficient　modulation　schemes,　the　modulated　signal　with　a　high　peak-to-average　power　ratio　(PAPR)　drives　the　power　amplifier　(PA)　to　operate　near　the　saturation　region　and　introduces　serious　nonlinearity　of　the　PA.　Digital　predistortion　(DPD)　is　one　of　the　most　promising　techniques　for　PA　linearization.　In　this　paper,　we　propose　a　low　complexity　extended　Kalman　filter　(LC-EKF)　algorithm　for　training　a　neural　network　(NN)　in　the　design　of　a　predistorter　for　a　DPD　system.　We　propose　a　method　to　decrease　the　matrix　dimensions　during　the　matrix　inversion　computation　of　the　Kalman　gain　using　the　matrix　inversion　lemma,　thereby　reducing　the　complexity　of　the　implementation　of　the　EKF　algorithm.　We　evaluate　the　proposed　LC-EKF　algorithm　for　the　neural　network　DPD　system　in　terms　of　both　complexity　and　performance.　The　simulation　results　show　that　the　proposed　LCEKF　algorithm　has　considerably　less　complexity　than　the　traditional　EKF　algorithm　without　sacrificing　its　performance　and　better　normalized　mean　squared　error　(NMSE)　and　adjacent　channel　power　ratio　(ACPR)　performance　than　the　Levenberg-Marquardt　(LM)　trained　neural　network　in　the　DPD　system.