Anthony Jessup (31 August 1928 – 19 December 1996) was an English first-class cricketer. Jessup was born in August 1928 at Blindley Heath. He later studied at Jesus College at the University of Oxford. While studying at Oxford, he played first-class cricket for Oxford University against the Free Foresters at Oxford in 1950. He played first-class cricket for Oxford until 1951, making a total of seven appearances. Playing as a slow left-arm orthodox bowler, he took a total of 19 wickets at an average of 22.73. He took a five wicket haul on three occasions and ten wickets in a match one, with best figures of 5 for 30 on debut against the Free Foresters. He took ten wickets in total in this match. Jessup died at Kensington in December 1996.