In this study, the changes in quality parameters and sensory-influencing parameters from the peel, red flesh, and white flesh of ‘Yonglian No.1′ peach fruits were analyzed during cold storage. The results indicated that the contents of total soluble solids (TSS), soluble sugar, organic acid, vitamin C, total anthocyanin, phenol, and flavonoids, as well as the good fruit rate varied depending on the storage stages and storage treatments. The peach fruits in MAP stored for 50 days had favorable exterior qualities, a good fruit rate of 100%, and a higher content of total soluble solids (TSS) at 12.6%. MAP was significantly effective at maintaining fruit firmness, the content of TSS, soluble sugar, organic acid, vitamin C, total anthocyanin, phenol, and flavonoids. Among the derivatives of anthocyanin, both cyanidin and pelargonidin were found in the peel, with a content of 33.45 mg/kg FW and 1.82 mg/kg FW, respectively. However, cyanidin was detected in the flesh with a content of 40.42 mg/kg FW. In the present work, the differences regarding phytochemical profiles and physical properties were mainly correlated with the storage stages and storage treatments of peach fruit. ‘Yonglian No.1′ had higher levels of health-promoting compounds during storage and maintained favorable quality.