We analyzed temporal and spectral properties, focusing on the short bursts, for three anomalous X-ray pulsars (AXPs) and soft gamma repeaters (SGRs), including SGR 1806−20, 1E 1048−5937, and SGR 0501+4516. Using the data from XMM-Newton, we located the short bursts by the Bayesian blocks algorithm. The short bursts’ duration distributions for three sources were fitted by two lognormal functions. The spectra of shorter bursts (< 0.2 s) and longer bursts (≥0.2 s) can be well fitted in a two blackbody components model or optically thin thermal bremsstrahlung model for SGR 0501+4516. We also found that there is a positive correlation between the burst luminosity and the persistent luminosity with a power law index γ = 1.23 ± 0.18. The energy ratio of this persistent emission to the time averaged short bursts is in the range of 10-103, being comparable to the case in Type I X-ray burst.