A new self-sustained divertor oscillation is discovered in magnetic island induced detached plasmas in the Large Helical Device. The divertor oscillation is found to be a self-regulation of the width of an edge magnetic island accompanied by detachment-attachment transitions. The modified Rutherford equation combined with an ad-hoc bootstrap current equation is introduced to describe the divertor oscillation as a predator–prey model between the magnetic island width and a remnant X-point bootstrap current. The model successfully reproduces the experimental observations in terms of the oscillation frequency, the phase relation between variables, and the oscillation amplitude.