Due to the existence of highly ordered hierarchical chiral structures, biological fibers and bundles such as tendons, ligaments, and climbing tendrils usually have excellent mechanical properties. How the hierarchical chiral structures affect the mechanical properties of fibers and bundles, however, remains unclear. In this paper, a theoretical model of the biological fibers and bundles with self-similar hierarchical chiral structures is developed by virtue of a simple homogenization treatment. Using the built model, the load transfer behavior and effect of material chirality, the chiral assembly forms, and structure level number on the mechanical properties are investigated. The results show that the mechanical properties of fibers and bundles are significantly dependent on the material chirality of fibrils and hierarchical chiral structures. The material chirality of fibrils can make the fiber much softer. And the hierarchical chiral structure provides the fibers and bundles with superior capability to endure large elongation and storage energy. The work is not only helpful for understanding the structure-property of biological fibers and bundles, but also for the design of artificial muscles and soft devices such as strain sensors.