The coalescence of stellar-mass primordial black holes (PBHs) might explain some of the gravitation waves (GWs) events detected by LIGO-Virgo-KAGRA. On the other hand, observational hints for supermassive PBHs (SMPBHs) have been accumulated. Thus it can be expected that stellar-mass PBHs might be gravitationally bounded to SMPBHs ($\sim10^{6}-10^9M_\odot$) in the early Universe, and both constituted primordial extreme mass-ratio inspirals (EMRIs). In this work, we initiate the study of the merger rate for primordial EMRIs. The corresponding intrinsic EMRI rate at low redshift may be comparable to that of astrophysical model, $10-10^4$yr$^{-1}$, which the space-based detector LISA has the capability to detect, but significantly raises with redshift. Though equal mass binaries also inevitably form, we find that under certain conditions the primordial EMRIs can be the most prevalent GW sources, and thus potentially a new probe to PBH.

23 pages, 6 figures