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Following the discovery of a black hole (BH) with a mass of 10^3-10^6 M(sun)in a starburst galaxy M82, we study formation of such a BH via successivemerging of stellar-mass BHs within a star cluster. The merging has a runawaycharacteristic. This is because massive BHs sink into the cluster core and havea high number density, and because the merging probability is higher for moremassive BHs. We use the Smoluchowski equation to study analytically theevolution of the BH mass distribution. Under favorable conditions, which areexpected for some star clusters in starburst galaxies, the timescale of therunaway merging is at most of order 10^7 yr. This is short enough to accountfor the presence of a BH heavier than 10^3 M(sun) in an ongoing starburstregion.Comment: 10 pages, no figures, to appear in The Astrophysical Journal  (Letters

Runaway Merging of Black Holes: Analytical Constraint on the Timescale