Cable-driven parallel manipulators and parallel continuum manipulators have attracted increasing attention in pick-and-place manipulation, owing to their low inertia and high safety. In cable-driven parallel robots, cables are utilized to control a moving platform, whereas parallel continuum manipulators employ flexible limbs. By combing these two types of mechanisms, the authors propose a novel flexible limb/cable hybrid-driven parallel continuum manipulator (HDPCM). The flexible limbs, equipped with their ability to withstand pushing forces applied on the moving platform, are a critical component of the HDPCM. Meanwhile, the cables, with their proficiency to modulate the shape of the flexible limbs and endure some of the pulling force, reduce the possibility of large divergence in flexible limbs. This results in an improved reachable workspace and load capacity for the manipulator. To predict the configuration of the proposed manipulator, an efficient kinetostatics analysis is given, utilizing a discretization-based approach. Among the infinitely many solutions to the inverse problem, the configuration with minimal potential energy is selected as the optimal solution. Finally, a prototype is fabricated, and validation experiments are conducted, which demonstrate that the prototype exhibits acceptable positioning accuracy and passive compliance. Furthermore, the proposed manipulator is validated to possess relatively superior performance in the workspace and load capacity.