  We analytically study electronic bound states around a single vortex core in
a noncentrosymmetric superconductor such as ${\rm CePt_3Si}$ without mirror
symmetry about the $ab$ plane. Considering a mixed spin-singlet-triplet Cooper
pairing model, we obtain a formula about the local density of states (LDOS)
around a vortex core in any directions of magnetic fields. The LDOS under a
magnetic field perpendicular to the c axis are quite different from those of
typical s-wave or d-wave superconductors. From the ellipticity of the spatial
pattern of the LDOS around a vortex core, one can estimate experimentally the
pairing symmetry of ${\rm CePt_3Si}$ such as the position of the gap nodes and
the ratio of the singlet component to the triplet component in order parameter.
