The prosecution said the offences came to light in September 2010.
Peter Donnelly, 69, from Castlewellan in Co Down, who was a curate at St Matthew's Church in Belfast, denies six charges of indecent assault and one of gross indecency alleged to have occurred between July 1983 and August 1987.
The prosecution said the offences came to light in September 2010 when the now 40-year-old woman reported to police how she was abused from the age of ten until she was 14.
When he was arrested by police and interviewed, Fr Donnelly claimed he could not remember the girl or her family and denied that he had in any way abused the girl.