The aim of this study was to identify the aromatic compounds present in different apple varieties and to gain insights into the changes in the aromatic compounds during ripening. Three apple varieties (“Red Astrachan”, “Ning Qiu”, and “Golden Delicious”) at different stages of ripening were selected for this study; their peel and pulp were analyzed via headspace solid-phase microextraction (HS-SPME)–gas chromatography–mass spectrometry (HS-SPME-GC-MS), and 30 volatile compounds were identified. The samples’ differences were analyzed using heat map cluster analysis, principal component analysis (PCA), and an independent samples t-test. The results showed that the content of aromatic compounds in the peel was higher than that in the pulp. The relative content of esters in the aromatic compounds of the three apple varieties followed the order of pulp > peel and “Ning Qiu” > “Golden Delicious” > “Red Astrachan”. This suggests that “Ning Qiu” combines the advantages of its parents in terms of its aroma content. The highest concentrations of aroma compounds in “Red Astrachan” and “Ning Qiu” accumulate before the ripening stage, and care should be taken to choose an appropriate harvesting time according to the different needs during production. The main compounds of “Red Astrachan” are aldehydes and C8 esters, while those of “Ning Qiu” and “Golden Delicious” are alkenes and esters. After analyzing the relative odor activity values (rOAVs) of key volatile compounds and their aroma descriptors during the harvest period, acetic acid pentyl ester, butanoic acid hexyl ester, hexanoic acid hexyl ester, and 2-ethyl-1-Hexanol were found to contribute the most to the overall flavor of the peel and pulp. “Ning Qiu” combines the parental advantages of the concentrated peel of “Red Astrachan” and the astringent pulp of “Golden Delicious”, with compounds in its composition that give a pleasing aroma. Mature “Ning Qiu” fruits have a more intense aroma and fruity flavor. The development of flavor-specific varieties has provided the theoretical basis for future research in molecular hybridization, molecular-assisted breeding, and the molecular biology of apple flavor synthesis and metabolism.