  Active optical clock, a new conception of atomic clock, has been proposed
recently. In this report, we propose a scheme of active optical clock based on
four-level quantum system. The final accuracy and stability of two-level
quantum system are limited by second-order Doppler shift of thermal atomic
beam. To three-level quantum system, they are mainly limited by light shift of
pumping laser field. These limitations can be avoided effectively by applying
the scheme proposed here. Rubidium atom four-level quantum system, as a typical
example, is discussed in this paper. The population inversion between
$6S_{1/2}$ and $5P_{3/2}$ states can be built up at a time scale of $10^{-6}$s.
With the mechanism of active optical clock, in which the cavity mode linewidth
is much wider than that of the laser gain profile, it can output a laser with
quantum-limited linewidth narrower than 1 Hz in theory. An experimental
configuration is designed to realize this active optical clock.
