A ratchet driven screwdriver with bits storage has a body. A ratchet driving device has a ratchet, a lever, a ratchet housing, a ratchet spring, two L-shaped ratchets, a steel ball and a compression spring. A bits storage has a spring seat, two torsion springs, a storage tube, an axis column, and a bits box. When replacing the bits, the back cover is pulled to drive the storage tube. Currently, a pressure of the two torsion springs can extend to a tapered end of the axis column to release a vertical force, and the back cover is pulled apart. The two torsion springs extend to the other end of the axis column, and the vertical force can make the bits box pushed to the open state and locked, so that an alternate screwdriver bit can be selected with turning the back cover.