Extracting fault-related features from noisy vibration signals is a pivotal prerequisite for condition monitoring of rolling element bearings. Multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) is a non-iterative blind deconvolution algorithm and has been proven as an efficient tool for periodic impulses extraction of rotating machinery. However, the effectiveness of MOMEDA strongly relies on the accuracy of the prior impulse period. Additionally, the MOMEDA method suffers from serious edge effect, resulting in the filtered signal shorter than the original signal. To solve these limitations of MOMEDA, a novel deconvolution algorithm called adaptive MOMEDA (AMOMEDA) is presented in this paper. The new method adopts a periodic modulation intensity (PMI) based strategy to automatically estimate the impulse period rather than a fixed prior period. The impulse period can gradually approximate the real fault-related period with the update of the filtered signal after every iterative step. To overcome the edge effect of MOMEDA, a waveform extension strategy is designed to adaptively restore the length of the filtered signal as the original signal according to the local characteristics of the signal at the left boundary. Simulated and experimental results of railway axle-box bearing demonstrated the effectiveness and superiority of AMOMEDA by comparison with MOMEDA. Moreover, the proposed method is compared with fast kurtogram and the improved complete ensemble empirical mode decomposition with adaptive noise to show that the proposed method is more effective.