Local mean decomposition (LMD) is widely used in the area of multicomponents signal processing and fault diagnosis. One of the major problems is end effects, which distort the decomposed waveform at each end of the analyzed signal and influence feature frequency. In order to solve this problem, this paper proposes a novel self-adaptive waveform point extended method based on long short-term memory (LSTM) network. First, based on existing signal points, the LSTM network parameters of right and left ends are trained; then, these parameters are used to extend the waveform point at each end-side of signal; furthermore, the corresponding parameters are adaptively updated. The proposed method is compared with the characteristic segment extension and the traditional neural network extension methods through a simulated signal to verify the effectiveness. By combing the proposed method with LMD, an improved LMD algorithm is obtained. Finally, application of rolling bearing fault signal is carried out by the improved LMD algorithm, and the results show that the feature frequencies of the rolling bearing’s ball and inner and outer rings are successfully extracted.