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Liquid 3He injected in a carbon nanotube is of high interests due to different behavior of the liquid helium in the quasi-one-dimensional systems. In this work, a variational approach has been performed to calculate some thermodynamic properties of this quantum system. In order to do so, a single-walled carbon nanotube containing liquid 3He is considered, applying the Lennard-Jones and Stan–Cole potentials for 3He–3He and 3He–C interactions, respectively. Finally the total energy, equation of state and incompressibility of the system have been calculated. Our calculations show the high values for the incompressibility at high densities, especially for high radii.