  We study the vortex zero-energy bound states in presence of pairing among the
low-energy Dirac fermions on the surface of a topological insulator. The
pairing symmetries considered include the $s$-wave, $p$-wave, and, in
particular, the mixed-parity symmetry, which arises in absence of the inversion
symmetry on the surface. The zero-mode is analyzed within the generalized
Jackiw-Rossi-Dirac Hamiltonian that contains a momentum-dependent mass-term,
and includes the effects of the electromagnetic gauge field and the Zeeman
coupling as well. At a finite chemical potential, as long as the spectrum
without the vortex is fully gapped, the presence of a single Fermi surface with
a definite helicity always leads to one Majorana zero-mode, in which both
electron's spin projections participate. In particular, the critical effects of
the Zeeman coupling on the zero-mode are discussed.
