The radiation density operator theory and perturbation method are used to obtain the master equation of the three-mode laser operation in a homogeneously broadened medium consisting of four-level atoms by means of a generalizasion of the Lamb fully quantum-mechanical theory. Meanwhile diagrams of probability flow are drawn. By considering and reasonablly understanding the principle of detailed balance, the equations of motion in steady states are obtained. The operation characteristics and the quantum-statistical properties of the lager under different conditions are discussed. Especially the calculations of the photon number distributions are carried out numerically, so that the results are given in detail and the comparison is easily carried out. Furthermore, by taking into account the equation of motion for the off-diagonal elements of the radiation density operator, the laser line-widths in different oases of gingle-mode, two-mode and three-mode are given and compared.