One of the purposes of this paper is to characterize congruences on P-regular semigroups by using P-congruence pairs, which is the P-gular version of congruence pairs fo regular semigroups. The other is to study congruences on a P-regular semigroup S with the same trace, the restriction of a congruence to the set of idempotents of S. Also the specialtypes of congruences on P-regular semigroups are observed.