Primordial black holes (PBHs) produced in the early Universe have attracted wide interest for their ability to constitute dark matter and explain the compact binary coalescence. We propose a new mechanism of PBH production during first-order phase transitions (PTs) and find that PBHs are naturally produced during PTs model-independently. Because of the randomness of the quantum tunneling, there always exists some probability that the vacuum decay is postponed in a whole Hubble volume. Since the vacuum energy density remains constant while radiation is quickly redshifted in the expanding Universe, the postponed vacuum decay then results in overdense regions, which finally collapse into PBHs as indicated by numerical simulations. Utilizing this result one can obtain mutual predictions and constraints between PBHs and GWs from PTs. The predicted mass function of PBHs is nearly monochromatic. We investigate two typical cases and find that 1) PBHs from a PT constitute all dark matter and GWs peak at $1$Hz, 2) PBHs from a PT can explain the coalescence events observed by LIGO-Virgo collaboration, and meanwhile GWs can explain the common-spectrum process detected by NANOGrav collaboration.
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