The extraction of flavanones such as naringin, narirutin, naringenin, hesperidin, and hesperetin from grapefruit peels was performed using subcritical water extraction (SWE), hot water extraction, and conventional methods such as methanol and ethanol extraction. We analyzed the total flavanone content using high-performance liquid chromatography (HPLC) for each extracting method. Among the three methods, SWE was the optimal method with optimal operating conditions of $170^{circ}C$ temperature and 10 min operating time. The maximum total flavanone extracted was $86.539{pm}3.52mg/g$ grapefruit peels. Moreover, we treated the extracts with 60% ${eta}$-cyclodextrin and then analyzed the surface structure of the encapsulated compounds by field emission-scanning electron microscopy (FE-SEM). The results indicated that the encapsulation in ${eta}$-cyclodextrin improved solubilization, and the inclusion complex could serve as food supplements.