We propose a new scenario for the evolution of a binary of primordial black holes (PBHs). We consider a dynamical friction by ambient dark matter, scattering of dark matter particles with a highly eccentric orbit besides the standard two-body relaxation process to refill the loss cone, and interaction between the binary and a circumbinary disk, assuming that PBHs do not constitute the bulk of dark matter. Binary PBHs lose the energy and angular momentum by these processes, which could be sufficiently efficient for a typical configuration. Such a binary coalesces due to the gravitational wave emission in a time scale much shorter than the age of the universe. We estimate the density parameter of the resultant gravitational wave background. Astrophysical implication concerning the formation of intermediate-mass to supermassive black holes is also discussed.
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