Studying the accretion process in very low-mass objects has important implications for understanding their formation mechanism. Many nearby late-M dwarfs that have previously been identified in the field are in fact young brown dwarf members of nearby young associations. Some of them are still accreting. They are therefore excellent targets for further studies of the accretion process in the very low-mass regime at different stages. We aim to search for accreting young brown dwarf candidates in a sample of 85 nearby late-M dwarfs. Using photometric data from DENIS, 2MASS, and WISE, we constructed the spectral energy distribution of the late-M dwarfs based on BT-Settl models to detect infrared excesses. We then searched for lithium and H$alpha$ emission in candidates that exhibit infrared excesses to confirm their youth and the presence of accretion. Among the 85 late-M dwarfs, only DENIS-P J1538317$-$103850 (M5.5) shows strong infrared excesses in WISE bands. The detection of lithium absorption in the M5.5 dwarf and its Gaia trigonometric parallax indicate an age of $sim$1 Myr and a mass of 47 $M_{rm J}$. The H$alpha$ emission line in the brown dwarf shows significant variability that indicates sporadic accretion. This 1 Myr-old brown dwarf also exhibits intense accretion bursts with accretion rates of up to $10^{-7.9}$$M_{odot}$ yr$^{-1}$. Our detection of sporadic accretion in one of the youngest brown dwarfs might imply that sporadic accretion at early stages could play an important role in the formation of brown dwarfs. Very low-mass cores would not be able to accrete enough material to become stars, and thus they end up as brown dwarfs.
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