Sodium-ion energy storage, including sodium-ion batteries (NIBs) and electrochemical capacitive storage (NICs), is considered as a promising alternative to lithium-ion energy storage. It is an intriguing prospect, especially for large-scale applications, owing to its low cost and abundance. MoS2 sodiation/desodiation with Na ions is based on the conversion reaction, which is not only able to deliver higher capacity than the intercalation reaction, but can also be applied in capacitive storage owing to its typically sloping charge/discharge curves. Here, NIBs and NICs based on a graphene composite (MoS2/G) were constructed. The enlarged d-spacing, a contribution of the graphene matrix, and the unique properties of the MoS2/G substantially optimize Na storage behavior, by accommodating large volume changes and facilitating fast ion diffusion. MoS2/G exhibits a stable capacity of approximately 350 mAh g−1 over 200 cycles at 0.25 C in half cells, and delivers a capacitance of 50 F g−1 over 2000 cycles at 1.5 C in pseudocapacitors with a wide voltage window of 0.1-2.5 V.