A celery cultivar, designated 51-7 IPS 1, is disclosed, the cultivar is, for larger frame size and heavier weight, short core length, savoyed and glossy leaf color, corky root rot resistance, no fringe burn on mature leaves and also yellower heart leaf color with solid midribs. The invention relates to the seeds of celery cultivar 51-7 IPS 1, to the plants of celery cultivar 51-7 IPS land to methods for producing a celery plant by crossing the cultivar 51-7 IPS 1 with itself or another celery cultivar. The invention further relates to methods for producing a celery plant containing in its genetic material one or more transgenes and to the transgenic celery plants and plant parts produced by those methods. The invention further relates to hybrid celery seeds, plants, and plant parts produced by crossing cultivar 51-7 IPS 1 with another celery cultivar.