We report on the observation of a helical Luttinger liquid in the edge of an InAs/GaSb quantum spin Hall insulator, which shows characteristic suppression of conductance at low temperature and low bias voltage. Moreover, the conductance shows power-law behavior as a function of temperature and bias voltage. The results underscore the strong electron-electron interaction effect in transport of InAs/GaSb edge states. Because of the fact that the Fermi velocity of the edge modes is controlled by gates, the Luttinger parameter can be fine tuned. Realization of a tunable Luttinger liquid offers a one-dimensional model system for future studies of predicted correlation effects.