  Obeying non-Abelian statistics, Majorana fermions holds a promise to
implement fault-tolerant quantum computing. It was found that Majorana fermions
can be simulated by the zero-energy excitation in a nanowire with strong
spin-orbit coupling interacting with an $s$-wave superconductor under a
magnetic field. However, the signal of Majorana fermion in that system is
obscured by the disorder in the nanowire and the confinement potential at the
wire end. Thus, more controllable platforms are desired to simulate Majorana
fermions. We here propose an alternative scheme to simulate the Majorana
fermions in a trapped-ion system. Our dimerized-ion configuration permits us to
generate the Majorana modes not only at zero energy but also at the nonzero
ones, which enlarge the family of Majorana modes and supply another qubit
carrier for quantum computing. We also investigate the controllability of the
Majorana modes by Floquet engineering. It is found that a widely tunable number
of Majorana modes are created on demand by applying a periodic driving on the
trapped-ion system. Enriching the platforms for simulating Majorana fermions,
our result would open another avenue for realizing fault-tolerant quantum
computing.
