Even after the woman asked 48-year-old Elliot Campbell to stop, he continued to send the messages.
Selkirk Sheriff Court was told that in April alone he sent 25 and eventually she reported the matter to the police.
Campbell pleaded guilty to sending the offensive messages from a house at Edderston Ridge, Peebles, between July last year and April.
He also admitted a second charge of intentionally causing another person to look at a sexual image without their consent.
Sentence was deferred for the production of a Criminal Justice Social Work Report and a Restriction of Liberty Order assessment until August 4.
He was also made subject to the notification requirements of the Sexual offences Act – the length of which will be determined at the sentencing hearing.