Celery (Apium graveolens L.) belongs to the Apiaceae family and biennial herbs. Celery is an important vegetable that is cultivated and consumed worldwide. Celery leaves, particularly the petioles, are the main edible parts. Seven genes (AgTCP1, AgTCP2, AgTCP3, AgTCP4, AgDELLA, AgLEP, and AgARGOS) that are involved in leaf growth and development were cloned from two celery cultivars (‘Liuhehuangxinqin’ and ‘Ventura’). The expression profiles of these genes were determined in different tissues and at three stages of leaf growth and development. Then, the petioles and leaf blades at the three stages were anatomically characterized. Results demonstrated that the seven genes were expressed in all tissues. The highest expression of all genes, except for AgLEP and AgTCP2, was found in the leaf blades, followed by the root, stem, and petioles. The relative expression of the genes in the petioles and leaf blades increased during the three stages. Higher gene expression was detected in ‘Ventura’ than in ‘Liuhehuangxinqin’. From Stage 1 to Stage 3, the collenchyma and vascular bundles of the petioles and leaf blades developed to be thick and large, the phloem and xylem developed extensively, and the cells grew large and tightly arranged. The growth and development of ‘Ventura’ were faster than those of ‘Liuhehuangxinqin’. The expression profiles of the seven genes (AgTCP1, AgTCP2, AgTCP3, AgTCP4, AgDELLA, AgLEP, and AgARGOS) and the anatomic characteristics of the petioles and leaf blades were used as bases to identify the related functions of potential genes at the different stages of leaf growth and development in celery. This study provided insights into the leaf regulation mechanism and development in the Apiaceae plant.