Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at the left and right ends of the chain in the Majorana-fermion representation. We also show this Majorana qubit in the spin representation and its advantage, over a single superconducting qubit, regarding quantum coherence. Moreover, we propose to use four superconducting qubits as the smallest system to demonstrate the braiding of Majorana modes and show how the states before and after braiding Majoranas can be discriminated.