  We theoretically investigate one-dimensional three-component
spin-orbit-coupled Fermi gases in the presence of Zeeman field. By solving the
Bogoliubov-de-Gennes equations, we obtain the phase diagram at given chemical
potential and order parameter. We show that the system undergoes a phase
transition from Bardeen-Cooper-Schrieffer superfluid to topological superfluid
as increasing the intensity of Zeeman field. By comparing to the two-component
system, we find, besides the topological phase transition from the trivial
superfluid to nontrivial topological superfluid, the system can always be in a
nontrivial topological superfluid, and there are two Majorana zero energy
regions while increasing the magnetic field. We find the three-component
spin-orbit-coupled Fermi gases in certain parameter range is more optimizing
for experimental realization due to the smaller magnetic field needed. We
therefore propose a promising candidate for realizing topological superfluid.
