  Extreme-mass-ratio-inspiral (EMRI) is one of the most important sources for
future space-borne gravitational wave detectors. In such kind of systems, the
compact objects orbit around the central supermassive black holes with
complicated trajectories. Usually, the trajectory is approximated as a geodesic
of a test-particle in Kerr space-time in a short duration, and the orbital
evolution is simulated with the help of adiabatic approximation. However, this
omits the influence of the compact object on the background. In the present
paper, employing effective-one-body formalism, we analytically calculate out
the trajectories of a compact object around a massive Kerr black hole with
generally three-dimension orbits and express the fundamental orbital
frequencies in explicit forms. In addition, by constructing an approximate
"constant" similar with the Carter constant, we transfer the dynamical
quantities such as energy, angular momentum and "Carter constant" to semilatus
rectum, eccentricity and orbital inclination with mass-ratio corrections. Our
formalism includes the first-order corrections of mass-ratio in the
conservative orbital motion in the extreme-mass-ratio limit. Changes of
frequencies due to the mass-ratio correction illustrate the test particle
approximation should be invalid for constructing the EMRI's waveform templates.
