Conventional twistable structures use discrete parts articulated around a number of linkages. These allow only a limited degree of twisting angle, are low in storage ratio, heavy and complex in morphing mechanisms. Double-helix structures are commonly applied to induce twistable shape-changing capability for deployable structures, these being capable of large axial deformations where prestressed thin-shell composite flanges or strips are employed; however, their structural stabilities are susceptible to thermal effects, and suffer from non-zero Gaussian curvature deformation induced by prestressing of the precured flat strips. Here, we propose a novel bistable helical structure, where zero Gaussian curvature deformation applies, and shows more stable and reliable morphing mechanics for a twistable structure to be engineered. This is achieved by exploiting bistable composite tape-spring (CTS) structures, where two CTS samples are pin-joined through spokes to formulate a helical structure. It is capable of large axial morphing, and stable in both the fully extended and twisted configurations, with adjustable storage ratio. A theoretical model was established to predict its bistability and a bespoke axial displacement rig was developed to investigate its non-linear morphing mechanisms in order to reveal the underlying fundamentals. These will facilitate torsional structural design for aerospace deployable structures.