According to reports, the woman was walking around Lizard Point Holiday Park on Sunday, March 24.
She was spotted between the hours of 5pm and 6pm.
It was at the same time that the two young children made their way into an arcade prompting a desperate search by the parents.
According to cops, a dad screamed "to let go" after seeing the woman holding the two kids.
The two youngsters then returned to their family safely.
Devon and Cornwall
Police have now issued a hunt to find the woman.
Cops said: "It is reported that two young children entered the arcade from the adjacent function room, and when the father of one of the children went to find them, he entered the arcade to find a woman unknown to him was holding each child by the arm.
"The father shouted for the woman to let go of the children, which she did. The children were then taken back to their families.