For　the　nonlinearity　of　high　power　amplifier　(HPA)　with　strong　memory　effects,　a　novel　HPA　predistortion　algorithm　based　on　adaptive　extended　Kalman　filter　and　neural　network　is　proposed.　In　the　predistortion　system　with　indirect　learning　architecture,　the　predistorter　and　HPA　inverse　estimator　are　modeled　with　the　same　real-valued　focused　time-delay　neural　network　(RVFTDNN),　and　the　extended　Kalman　filter　(EKF)　is　used　to　iteratively　train　and　update　the　coefficients　of　the　neural　network.　It　is　concluded　that　Levenberg-Marquardt　(LM)　algorithm　is　a　special　case　of　EKF　algorithm　in　theory.　The　stably　convergence　condition　of　EKF　training　algorithm　is　analysed　with　the　Lyapunov　stability　theory　and　adaptive　covariance　matrix　of　measurement　noise　is　derived　for　iterative　computation.　Simulation　results　show　that　compared　with　LM　algorithm　the　training　error　and　generalization　error　of　adaptive　EKF　predistortion　algorithm　are　both　less.　The　adjacent　channel　power　ratio　(ACPR)　of　HPA　output　signal　with　adaptive　EKF　predistortion　is　better　than　that　of　LM　predistortion　by　2　dB.　Copyright　©　2016　Acta　Automatica　Sinica.　All　rights　reserved.