We cooled cesium atoms below the Doppler cooling limit by laser cooling. For this deep cooling of atoms, the laser frequency was shifted by using the Zeeman shift of an absorption line of cesium. The stabilization of the laser frequency was maintained while the laser frequency was shifted by 40 MHz within 2 ms. The lowest temperature of the laser-cooled cesium atoms was $2.2muK$pm$0.5$muK$</TEX>in this experiment. We measured the temperature of the laser-cooled cesium atoms as a function of the frequency detuuing and the intensity of the cooling laser. The results agreed well with the ones calculated by two-photon laser cooling theory.theory.