  We demonstrate the trajectory measurement of the single neutral atoms
deterministically using a high-finesse optical micro-cavity. Single atom
strongly couples to the high-order transverse vacuum TEM_{10} mode, instead of
the usual TEM_{00} mode, and the parameter of the system is (g_{10},\kappa
,\gamma )=2\pi \times (20.5,2.6,2.6)MHz. The atoms simply fall down freely from
the magneto-optic trap into the cavity modes and the trajectories of the single
atoms are linear. The transmission spectrums of atoms passing through the TEM10
mode are detected by a single photon counting modules and well fitted. Thanks
to the tilted cavity transverse TEM10 mode, which is inclined to the vertical
direction about 45 degrees and it helps us, for the first time, to eliminate
the degenerate trajectory of the single atom falling through the cavity and get
the unique atom trajectory. Atom position with high precision of 0.1{\mu}m in
the off-axis direction (axis y) is obtained, and the spatial resolution of
5.6{\mu}m is achieved in time of 10{\mu}s along the vertical direction (axis
x). The average velocity of the atoms is also measured from the atom transits,
which determines the temperature of the atoms in magneto-optic trap, 186{\mu}K
{\pm} 19{\mu}K.
