The 19-year-old girl from Dulariya village was in a relationship with 25-year-old Rajat, from neighbouring village, police said.
The incident took place this morning when the girl's family members found the couple in an objectionable position, Station Incharge of Raja Ka Rampur Police Station R K Tiwari said.
Enraged, they shot them dead, he said.
Tiwari said the bodies have been sent for post-mortem and the country made firearm used in the double murder has been recovered.