We report the tubular shape of molybdenum sulfide selenide (MoSSe) alloy on the carbon nanotubes (CNTs) as lithium (Li) storage materials. Two to five layers of MoSSe alloy have an interlayer spacing of ~6.6 Å and coaxially coat the CNT. After Li ion is intercalated to the MoSSe layers, Li2S, Li2Se, and metallic Mo nanoparticles are irreversibly deposited on the CNT electrodes by a chemical conversion process. Galvanostatic cycling tests perform Li2S/Li2Se faradaic reaction at ~2.2 V vs. Li/Li+ and capacitive processes below ~1.3 V arising from physical adsorption of Li+ on Mo, Li2S, and Li2Se nanoparticles, and electrolyte decomposition. As a result, tubular MoSSe/CNT electrodes exhibit stable cyclability for over 200 cycles, the capacity of 663 mAh g−1, and excellent rate capability that is two-fold greater at 20 A g−1 than that of the MoS2 sheet partially wrapping the CNT. It is attributed to stable Li2S/Li2Se redox reaction without any dissolution of polysulfides/polyselenides, respectively, low charge-transfer resistance, and retardation of electrolyte decomposition. These findings suggest that the tubular MoSSe/CNT nanocomposites act as promising electrodes for hybrid-ion capacitors.