Agarwood is a resinous wood of Aquilaria species and has been used for various applications. Burning agarwood incense is a common practice in temples and homes in Asia. Kynam is widely regarded as high-quality agarwood in the market. Recently, cultivated grafting Kynam (CGK) has emerged as a new agarwood product in the market, which greatly affects the price of high grading Kynam agarwood. In this study, the morphology, ethanol extract content, and incense chemical profile of CGK was investigated and compared with those of wild Kynam (WK) and cultivated common agarwood (CCA). The incense smoke of CGK was analyzed by thermogravimetric Fourier transform infrared spectroscopy (TG-FTIR) and headspace gas chromatography-mass spectrometry (HS-GC-MS). The results showed that the heating of most incenses occurred below 200 °C, and the mass-loss rate value of CGK was between those of WK and CCA. The HS-GC-MS analysis showed the chemical compounds of incense smoke of CGK at 40, 100, and 180 °C, corresponding to the head, middle, and tail of the heating process, respectively. The results suggested that the sesquiterpenes compounds were the major contributors to the mysterious and elegant odoriferous character of agarwood incense. However, a peak area percentage analysis revealed a significant difference in the predominant compounds between CGK and WK, especially at lower temperatures. Therefore, it is not straightforward to substitute WK with CGK. The results are helpful for the study and usage of the new cultivated grafting Kynam agarwood and the development of the agarwood incense industry.