Cable-driven tensegrity mechanisms can be considered to control at the same time position and stiffness. Adequate control solutions have however not been proposed yet. This paper thus focuses on the development of an original control strategy using a tension distribution algorithm adapted from related work on cable-driven mechanisms. The algorithm is being used to modify the mechanism configuration together with its stiffness through the level of prestress in the system, which constitutes a step toward the exploitation of such mechanisms for variable stiffness applications. Simulations show encouraging results on the stiffness variation capacity of the presented mechanism.