Eric Roe, 70, waged a prolonged campaign of sexual abuse against the girl which went unreported for years, York Crown Court heard.
On Monday, following a week-long trial, the jury unanimously found Roe guilty of 13 separate charges, including indecency with a child and causing a child under 13 to engage in sexual activity.
The offences dated back many years, when Roe was in his 50s, but the victim did not come forward to police until 2018.
The offences occurred at a property in Scarborough.
The victim, who cannot be named for legal reasons, underwent counselling and sought help from her doctor as she got older after showing signs of distress and being “visibly upset”.
Judge Simon Hickey said Roe’s campaign of abuse had “effectively destroyed (the victim’s) life”.
He told the pensioner he would be remanded in custody until the sentence hearing next month.
Roe, of Commercial Street, Scarborough, was led down to the cells by a dock officer.
He will learn of his fate on April 8.
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