  Constructing qubits which are suitable for quantum computation remains a
notable challenge. Here, we propose a superconducting flux qubit in a dc SQUID
structure, formed by a conventional insulator Josephson junction and a
topological nanowire Josephson junction with Majorana bound states. The zero
energy Majorana bound states transport $4\pi$ period Josephson currents in the
nanowire junction. The interplay between this $4\pi$ period Josephson effect
and the convectional $2\pi$ period Josephson effect in the insulator junction
induces a double-well potential energy landscape in the SQUID. As a result, the
two lowest energy levels of the SQUID are isolated from other levels. These two
levels show contradicting circulating supercurrents, thus can be used as a flux
qubit. We reveal that this flux qubit has the merits of stability to external
noises, tolerance to the deviation of system parameters, and scalability to
large numbers. Furthermore, we demonstrate how to couple this flux qubit with
the Majorana qubit by tuning the junction parameters, and how to use this
coupling to manipulate the Majorana qubit.
