A dual-gate InSb nanosheet field-effect device is realized and is used to investigate the physical origin and the controllability of the spin-orbit interaction in a narrow bandgap semiconductor InSb nanosheet. We demonstrate that by applying a voltage over the dual gate, efficiently tuning of the spin-orbit interaction in the InSb nanosheet can be achieved. We also find the presence of an intrinsic spin-orbit interaction in the InSb nanosheet at zero dual-gate voltage and identify its physical origin as a build-in asymmetry in the device layer structure. Having a strong and controllable spin-orbit interaction in an InSb nanosheet could simplify the design and realization of spintronic deceives, spin-based quantum devices and topological quantum devices.