It was founded by the Presentation Sisters of Staten Island in September 1962 and named for Mary Young Moore (not to be confused with Maryland governor Wes Moore), a beneficiary to the Roman Catholic Archdiocese of New York,[1] and was the first archdiocesan high school for girls on Staten Island.

[4] In 2005, Moore initiated a program called Presentation Scholars Academy for gifted students.

The school has several annual events: Freshman Field Day, Senior Costume Day, Junior Prom, Senior Prom, Hall of Fame Dinner and Golf Outing, Performing Arts Dinner Cabaret, Coaches for Cancer Basketball Tournament, Fall play, Christmas Spectacular and Spring musical, Dance and Music Recitals.

Moore Catholic offers basketball, baseball, football, softball, lacrosse, soccer, co-ed cheerleading, bowling, and track and field, and Nick Giannatasio is the Varsity Football Coach.

Moore Catholic is staffed by the Daughters of Our Lady of the Garden, and dedicated lay faculty and staff.